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TABLE OF CONTENTS

1 Basics & Beyond............................................ .................................................. ........... 4

1.1 Introduction...................................... .................................................. .................4

1.2 The EXCEL Screen............................................ ................................................. 4

1.3 Moving Around............................................ .................................................. .....5

2 Data Entry .................................................. .................................................. ............... 8

2.1 Text .................................................. .................................................. .................8

2.2 Number (including date, time, percent) .................................................. ............ 8

2.3 Formulae .................................................. .................................................. .........8

2.4 Functions......................................... .................................................. ..................9

2.5 AutoComplete .................................................. .................................................. .9

2.6 AutoCorrect....................................... .................................................. ..............10

2.7 AutoFill.......................................... .................................................. .................10

2.8 Data Validation .................................................. ...............................................11

3 Totals & More.............................................. .................................................. ........... 13

3.1 + + + ,…. why not? .................................................. ......................................... 13

3.2 SUM() Function.......................................... .................................................. ....13

3.3 QuickSum .................................................. .................................................. .....13

3.4 SUBTOTAL() Function.......................................... ..........................................14

3.5 SUMIF() Function .................................................. ..........................................14

3.6 Sorting Data .................................................. .................................................. ..14

3.7 Sub-Totals............................................ .................................................. ...........15

3.8 Conditional Sum Add-In................................................ ...................................16

4 Queries in Lists .................................................. .................................................. ..... 17

4.1 AutoFilter........................................ .................................................. ................17

4.2 Advanced Filter............................................ .................................................. ...17

5 Functions......................................... .................................................. ........................ 19

5.1 Lookup Functions .................................................. ...........................................19

5.2 Date Functions .................................................. ................................................19

5.3 Numeric Functions......................................... .................................................. .21

5.4 Text Functions .................................................. ................................................21

5.5 Financial Functions......................................... .................................................. 21

5.6 Some more functions .................................................. ......................................22

6 The Look & Feel of Output .................................................. .................................... 24

6.1 Formatting........................................ .................................................. ...............24

6.2 Styles............................................ .................................................. ...................25

6.3 Conditional Formatting........................................ .............................................26

6.4 Custom Views............................................. .................................................. ....26

6.5 Printing.......................................... .................................................. ..................27

6.6 Saying it with Charts............................................ ............................................. 27

7 Copying & Moving............................................ .................................................. ..... 28

7.1 Paste Special .................................................. .................................................. .29

8 Saving Work & Protecting It .................................................. .................................. 30

8.1 File-Level Protection .................................................. ......................................30

9 Analysing Data.............................................. .................................................. .......... 32

9.1 Data Tables .................................................. .................................................. ...32

9.2 Scenarios......................................... .................................................. ................33

9.3 Goal Seek.............................................. .................................................. ..........33

9.4 Solver............................................ .................................................. ..................33

10 PivotTables .................................................. .................................................. .......35

10.1 Creating a Pivot Table .................................................. .................................... 35

10.2 Layout of the PivotTable .................................................. ................................ 37

10.3 Some Examples:......................................... .................................................. ..... 37

11 Auditing Tools .................................................. .................................................. ..41

11.1 Auditing Toolbar........................................... .................................................. .. 41

11.2 Documenting a Sheet .................................................. ...................................... 41

11.3 Migrating Data from Other Software.......................................... ...................... 43

11.4 Common Audit Techniques .................................................. ............................ 43

12 Automating MS-EXCEL .................................................. ....................................44

12.1 Open EXCEL each time computer starts .................................................. ........ 44

12.2 Open a particular file each time EXCEL starts............................................ ..... 44

12.3 Create a new file based on a template each time computer starts..................... 44

12.4 Specifying the Defaults in EXCEL............................................. ...................... 44

12.5 Customizing Menus & Toolbars.......................................... ............................. 45

12.6 Customization Options........................................... ........................................... 46

12.7 Templates......................................... .................................................. ............... 46

12.8 Workspaces........................................ .................................................. ............. 47

12.9 Talking with Other Software .................................................. .......................... 47

13 Introduction to Macros............................................ .............................................. 48

13.1 Global Macros vs. Individual Macros............................................ ................... 48

13.2 Use of Macro Recorder.......................................... ........................................... 49

13.3 Running Macros............................................ .................................................. .. 49

13.4 Basics of VB Programming .................................................. ............................ 51

1 ANNEXURE A: KEYBOARD SHORTCUTS......................................... ............... 53

2 ANNEXURE “B” IMPORTANT EXCEL FUNCTIONS........................................ 55

3 ANNEXURE “C”: COMMON ERROR CODES .................................................. .. 59

4 ANNEXURE “D” LIST OF ADD-INS PROVIDED WITH MS-EXCEL .............. 61

1 Basics & Beyond..

1.1 Introduction

Microsoft Excel is a spreadsheet program that is designed to record and analyze numbers

and data. Excel is very widely used for accounting and financial purposes.

The files created in Excel are known as workbooks. In turn, each workbook can contain

one or more worksheets. An Excel worksheet is laid out like a grid with horizontal rows

and vertical columns. Columns are labeled with alphabets (A, B, C, etc.) while rows are

given numbers (1, 2, 3, etc.). The intersection of a row and a column is called a cell. A

cell is referred by a combination of column alphabet and row number (A1, A2, etc.). A

cell is a primary unit of measure in Excel and all the information is stored in cells. . A

range is a collection of contiguous cells (which form a rectangular block) on which the

user wants to perform similar type of calculations. A range is referred to by a

combination of the cell addresses of the diagonally opposite cells separated by a colon

(A1:D6)

1.2 The EXCEL Screen

On loading MS-EXCEL (either through the shortcut menu, or icon on desktop or through

the Start Menu), the following screen appears:

The various components of the EXCEL Screen are explained in brief below:

Sr. Contains Remarks

1 Title Bar Contains the name of the File currently open and also has

the window control buttons to either close or minimize the

program0

2 Menu Bar Contains the list of various commands that can be

performed in MS-EXCEL. It can be invoked either by a

mouse click or the Alt Key from the keyboard

3 Tool Bars Contain buttons for some commonly performed tasks. The

commands can be activated by a mere mouse-click

4 Formula Bar Displays the content of the active cell. The left hand side of

this bar includes the name box which contains the list of all

the range names and thereby facilitates quicker worksheet

navigation

5 Column Labels Contains the headings of the columns. Can be used for

column-wide operations like increasing column width,

hiding columns, formatting entire columns, etc.

6 Row Labels Contains the headings of the rows. Can be used for rowwide

operations like increasing row height, hiding rows,

formatting entire rows, etc.

7 Sheet Area The place where the actual data is entered. The Active Cell

is surrounded by a dark rectangle.

8 Sheet Tab Gives reference to the sheet which is currently active. One

can quickly navigate through different sheets from here

9 Additional Tool

Bars

Some additional toolbars

10 Status Bar Includes the various information sent by EXCEL. Of

particular use is the QuickSum Feature in the status bar

which automatically displays the totals of the selected cells

11 Scroll Bars &

Split Indicator

The Scroll Bars can be used for quick movement within a

worksheet. The extreme top of the vertical scroll bar and

the extreme right of the horizontal scroll bar contain a split

indicator which permits the user to divide the sheet into

two parts.

12 Application

Control Buttons

These buttons are used to minimize or control the size of a

particular file.

The cell A1 is surrounded with dark rectangular block. It is the active cell. Any entry of

data is made into the active cell.

1.3 Moving Around

A worksheet can contain upto 65,536 rows and 256 columns whereas the visibility of the

information on the screen is restricted to the size of the screen (generally 18-20 rows and

8-10 columns are visible at a time). Therefore, one may need to move around different

sections of a worksheet. There are various ways in which one can move around very

efficiently.

1.3.1 Keyboard Shortcuts

The most widely used option is of course a wheel-mouse but at times, the keyboard is

very handy. For example, to reach the last entered cell in a worksheet one just uses the

<Ctrl>+<End> combination. Similarly, <Ctrl>+<Home> takes one to the first cell of the

worksheet (which is always A1). Using <Home> takes one to the first cell of the

particular row. <End> can be used with the combination of the arrow keys to reach at the

end of the list in the particular direction. A complete list of keyboard shortcuts is

provided in Annexure “A”

1.3.2 Range Names

Sometimes it is convenient to use a descriptive name to name a cell or a range of cells.

Named ranges can also be used in formulas and functions. To name a range:

1. Select the range to be named.

2. Click the Name box on the left side of the formula bar

3. Type the range name (up to 255 characters). Valid names cannot use spaces

and the first character must not be a number. Also, the name cannot look like

a cell address such as B14.

4. Press Enter.

OR

1. Select the range

2. Select Insert/Name

3. Choose Define

4. Type the name of the range.

Once a particular range has been named, reaching that particular cell is very easy. Just

choose the range name from the Name Box and you are taken there.

1.3.3 Window Split & Freeze

Many a times, one wants to refer to two different sections of a worksheet. For example,

in case of a long list, the headings might scroll up. In that event, one can consider to split

the window into two parts. One can split the windows by dragging the split handle which

appears at the extreme top of the vertical scroll bar and the extreme right of the horizontal

scroll bar. In the alternative, one can position the cell pointer to the cell where one desires

a split and choose the command Split from the Window Menu. To remove the split, either

re-drag the split bar or choose Window->Unsplit.

While the movement of the split windows is synchronized, none of them is fixed.

Therefore, it is possible to loose track of the titles if the mouse movements are not

properly handled. To avoid such a situation, one can choose Window->Freeze Panes.

To reverse the process, choose Window->Unfreeze Panes.

1.3.4 Multiple Windows

Windows Split does not permit asynchronous viewing. For such a purpose, one can

consider opening multiple windows of the same file. To do this, choose Window-> New

Window. Re-size both the windows using the mouse pointer. Of course, multiple

windows of the same file are at times confusing to handle.

2 Data Entry

Information entered into a cell is understood either as a text entry, a value or a formula.

Functions are also treated equivalent to formulae. Dates, time and percentages are stored

as numbers (values). It is important that a particular information is stored in the correct

format.

2.1 Text

Text entries or labels can contain any combination of letters, numbers and spaces. A label

which is too long for the width of a cell floats across the cells to its right / left / both

(depending on the alignment of the cell) as long as those cells do not contain any

information. If the cells aren’t empty, the label is truncated or cut-off. By default, labels

are left-justified.

2.2 Number (including date, time, percent)

Numbers and text are treated differently. The default alignment for text is left whereas for

numbers, it is right. Secondly, if a value is too large to fit in the current cell width, Excel

displays a series of # characters as a error signal. A list of various error signals and what

they denote is enclosed as Annexure “C”. Values are displayed in the General Number

Format. This display can be customized using the Format Cells command.

2.3 Formulae

A cell can also derive the value though a formula. The building of a formula is intuitive

and can be easily mastered through practice. For example, if Cell A1 contains 3000 being

the tax payable and you want to calculate the surcharge, go to Cell A2 and type the

formula +A1*5% (as the surcharge rate is 5%) and Excel does the calculation for you. To

get the gross tax liability, go to Cell A3 and say +A1+A2 (as gross tax includes tax and

surcharge). The formula can also be built by pointing to the dependent cells instead of

typing the cell address. Excel evaluates a formula in a particular order of precedence.

The operators used in a formula and precedence accorded by EXCEL are as under:

Operator Description Precedence

: Range of Cells 1

, Union of Cells 2

% Percentage 3

^ Exponentiation 4

* Multiplication 5

/ Division 6

+ Addition 7

- Subtraction 8

& Concatenation 9

= < > Comparison Operators 10

If the order of evaluation is to be changed, parenthesis should be used to group

expressions within a formula. If more than one pair of parenthesis is present in a formula,

Excel evaluates the expression in the innermost parenthesis first.

2.4 Functions

A cell can also derive its value through functions. Functions are processes, which have

been defined and standardized by Excel. A complete list of functions can be found at

Insert -> Function. A list of commonly used functions is enclosed as “Annexure B”. Few

more common functions include the SUM function (which totals all the numbers in a

particular range – of course, EXCEL also has the QuickSum Feature which displays the

sum of the selected range in the bottom pane) and the IF function used to manage

alternate calculations in varying situations (it is very simple to use and can be nested, but

take care to use the brackets appropriately otherwise the results can be disastrous!). A

very common example of the use of IF function is to calculate the tax payable by an

individual. For example, if cell B3 contains the net taxable income of an individual, the

tax payable by him (excluding surcharge) can be calculated using a nested IF function as

stated: =IF(B3>150000,(+B3-150000)*0.3+19000,IF(B3>60000,(B3-60000)*0.2+1000,

IF(B3>50000,(B3-50000)*0.1,0)))

2.4.1 Using the Function Builder

A function takes in certain standard arguments, undertakes the evaluation process and

returns a particular result. In case one is unaware of the arguments, one can type the

function name along with the opening parenthesis and click on the = sign on the Formula

Bar. The Function Wizard presents the list of arguments and the brief description of the

arguments. In such a fashion, one can build a formula through a Wizard and

simultaneously learn the function itself. For example, the Function Builder Dialog Box in

the case of PMT function is shown below:

2.5 AutoComplete

Manual data entry into a range of cells can be made faster with the assistance of

AutoComplete - a feature which suggests the current cell entry based on the existing list.

It should however be noted that AutoComplete has certain limitations – it does not work

if there is a blank cell in the list, it works only when a unique combination consisting of

at least one alphabet is met in the list. In case of multiple similar entries, a better option is

the Pick from List which appears in the right-click shortcut of the mouse.

2.6 AutoCorrect

The AutoCorrect feature automatically corrects common typing errors as you type. For

this purpose, Excel uses a database of commonly misspelled words. This database can be

customized from the Tools -> AutoCorrect Menu. The following screen comes up:

One can use the AutoCorrect feature to quickly type some normal text which is regularly

used in an organization. For example, the organization name can be made a subject

matter of AutoCorrect to speeden up data entry.

2.7 AutoFill

AutoFill is an in-built feature whereby one can fill up a particular range of cells based on

some pre-determined series. For example, if one cell contains January and the next one

contains February, one can just use the fill handle to automatically complete the entire

range with the month names. One can create custom lists pertaining to one’s organization

(for example, plant locations) from Tools -> Options -> Custom Lists. The following

screen appears where one can either type in the required items or pick from a range of

cells

2.8 Data Validation

At times, there may be a need to restrict the content that is being typed into a particular

cell. For example, one may want the residential status to be either “Resident” or

“Resident but Not Ordinarily Resident” or “Non Resident”. In such a case, the entry into

a particular cell can be validated through the “Data Validation” Feature. The steps for

data validation feature are explained below:

1. Select the cell/range for which validation is to be applied

2. Choose Data -> Validation from the menu. The following screen appears

3. This feature validates only Keyboard Input that too in cases where the

entry is made after the validations are set and hence may have limitations

4. The user can choose the type of data and the range of data (which may be

open-ended from one side). Alternatively, the user can specify a predefined

list to choose from

5. The user can also specify the action to be taken in case the data entered is

invalid

�� ”STOP” does not permit entry of invalid Data

�� “WARNING” allows alteration to invalid data. The user may still

continue with the invalid data

�� “INFORMATION” just informs about the invalid data

�� Unchecking the “CHECK BOX” on the top allows entry of invalid

data without any disturbance

6. The Auditing Toolbar (Tools -> Auditing -> Show Auditing Toolbar)

contains icon which enables the circling of invalid data for attention

(second last icon on the toolbar)

3 Totals & More..

Totalling is one of the basis requirement of any spreadsheet application. Consider the

situation wherein the information of daily sales is entered in column B from rows 2 to 8.

We are interested in calculating the weekly sales.

3.1 + + + ,…. why not?

One of the ways to calculate the weekly sales would be to use the formula

+B2+B3…+B8. This however is not the ideal means for multiple reasons:

1. The length of the formula can become prohibitive

2. If one of the cells is later deleted, the result would display an error message

3. If an additional cell is later inserted, the value therein would not figure in the total

3.2 SUM() Function

The ideal way to total a particular range of numbers is therefore to use the SUM()

function. The standard usage of the SUM function has already been considered. Of

importance to note is the fact that one can total multiple non-contiguous ranges using a

single SUM function. Just separate the range addresses by a comma. One can also use

range names instead of the cell attributes to make the function more meaningful for the

users.

3.3 QuickSum

Many a times, one just wants to refer to the total of a particular range of cells. For this

purpose, one need not insert the SUM function and delete it thereafter. MS-EXCEL

presents built-in totals on selection of a range at the status bar which appears at the

bottom of the sheet. Even the Quicksum feature can be customized to show either the

total or the maximum, minimum, average, count, numeric counts and so on. To customize

the Quicksum feature, rightclick at the place where the sum is displayed and the

following options appear:

Choose the relevant option. For example, if I am interested in finding the maximum value

in a particular range, I shall choose Max.

3.4 SUBTOTAL() Function

In case there are nested totals, the SUM function can create havoc as there would be

multiple totals. In such a situation one can consider the use of SUBTOTAL() function.

This function avoids the cascading effect of the SUM function by recognizing the multilayered

totaling feature. Accordingly, a subtotal function ignores the value of another

subtotal function in the selected range of cells. The subtotal function is not restricted

merely to the summation but can also be used for counts, etc. Accordingly, the

SUBTOTAL() Function requires an additional argument which is the function number.

The various function numbers and the action performed by them are tabulated below:

Function Number Action

1 AVERAGE

2 COUNT

3 COUNTA

4 MAX

5 MIN

6 PRODUCT

7 STDEV

8 STDEVP

9 SUM

10 VAR

11 VARP

Accordingly, to get a subtotal of the cells in A2 to A9, one will use the function

=SUBTOTAL(9,A2:A9)

3.5 SUMIF() Function

There might be situations wherein one wants to total only particular values within a list.

In such a scenario, one can use the SUMIF() Function. This function evaluates the values

for a specific condition and accordingly includes them for summation. The arguments for

the SUMIF Function are:

Criteria Range: The range specifying the parameter or the condition

Criteria: The exact condition

Sum Range: The values to total

A cousin of SUMIF() Function is the COUNTIF() Function which counts the number of

cells satisfying a particular criteria. In fact, the COUNTIF() Function can be combined

with the Data Validation Feature to effectively stop the input of duplicate entries within a

range of cells.

3.6 Sorting Data

In case a list of data is typed, one may need the data arranged in a particular fashion. For

example, you may want your client details either alphabetically or based on the client

codes. This is where sorting is useful and the same is very simple. Choose the relevant

command from the Data Menu and the Sort Wizard takes you through the rest of the

process. Remember, sorted data is always advantageous from three counts: firstly, it

improves readability, secondly, it permits effective lookups and lastly, it lays down the

foundation for data grouping and sub-totalling.

�� Sorting is a permanent process as compared to filtering which is a temporary process

�� Choose any cell in the data range and Select Data -> Sort

�� Choose successive sort keys and sort order

On a brief review of the above screen, one understands that the sort function permits

sorting only upto three levels of data. If sorting is required for multiple levels of data,

then one will have to use the sort function more than once. Sort first based on keys of

least significance and move to keys of higher significance.

3.7 Sub-Totals

At times, there is a need to not only have grand totals but also subtotals – would you not

like to have group-wise outstanding as well as total outstanding? For this purpose, one

can use the Subtotals Function in the Data Menu. The Function is versatile and permits to

have multiple levels of subtotals (for having such multiple levels, do not replace the

current subtotals). Only care required is to sort the list in the same order of subtotalling

before using the subtotals command otherwise you might end up in a mess. One can also

consider the use of page-break option if you want individual reports for individual

groups. And if things appear messy, just remove all subtotals and Start Afresh!

To subtotal data in a spreadsheet follow these steps:

1. Decide upon the column you wish to use for the subtotal.

2. Sort the data using the criterion you selected in step 1.

3. Select Data/Subtotal. Complete the subtotal window that appears and click

OK.

4. Subtotals will now appear in the spreadsheet. Subtotals can be isolated from

raw data using the gray view bar to the left. Clicking the (-) boxes will reduce

data, clicking the (+) box will restore data.

5. Clicking the small 1,2,3, boxes in the upper left corner will reduce or expand

all categories of data simultaneously.

6. To remove subtotals select Data/Subtotal and click on the “Remove All”

button.

3.8 Conditional Sum Add-In

The SUM function is too simplistic in the sense that it does not permit multiple layering

nor does it accept conditions. The SUBTOTALS feature permits multiple layering but is

highly inflexible in approach. To incorporate complicated and specialised tasks,

Microsoft Excel ships with certain add-ins. Each add-in performs certain tasks and has to

be loaded specifically before it can be used. A complete list of add-ins is given in

Annexure “D”. The process of loading an add-in is simple. For conditionally totalling a

particular list, consider the use of the Conditional Sum Wizard Add-in. The Wizard is too

simple to be true!

�� Choose Tools -> Wizard -> Conditional Sum

�� Select the list as the range, select the value to sum and specify criteria

�� To make the function dynamic, copy both the formula and condition

4 Queries in Lists

4.1 AutoFilter

In case of multiple records and large databases, there may be a need to restrict the report

to certain types of transactions. For example, if you are maintaining your sale details in

MS-EXCEL, you may be interested in a quick list of all the sales made to a particular

customer. This requirement is known as a query. Again, Excel has an excel-lent (!)

feature to do this. One just needs to use it to believe it. Yes, we are talking of AutoFilter –

the feature which displays a subset of data without actually sorting or moving data. Once

you select the AutoFilter command from the Data Menu, Excel inserts drop down arrows

next to column headings in the list. Selecting an item from a drop down list hides all rows

except rows that contain the selected value. One can edit and format the cells which are

visible.

�� Choose any cell in the data range and Select Data -> Filter -> AutoFilter

�� Use the drop down lists to specify criteria. Criteria can be

1. Particular Value

2. Top/Bottom (no of items) in terms of value or percentage

3. Range through Custom Criteria

4. Blanks/ Non-Blanks

�� Various criteria in differing columns are cumulative (AND) condition

�� Remove criteria in specific column by choosing “All” from the drop down list

�� Remove criteria in all columns by choosing Data -> Filter -> Show All

4.2 Advanced Filter

The filtered data can also be copied into another area by the simple process of copy-paste.

One limitation of AutoFilter is that one can have multiple alternative criteria (OR

condition to be more specific) for a single field, one can also have cumulative multiple

criteria (AND condition) across multiple fields but one cannot have alternative multiple

criteria across various fields. To cover such complex searches, one has to take recourse to

the Advanced Filter Option. Here, one specifies the conditions in a separate range known

as the criterion range. The results can be filtered in the original list or in another range of

cells.

�� Useful for specifying criteria which are alternative in nature (OR) condition

�� Make use of a “criteria range”

�� Select Data -> Filter -> Advanced Filter

�� The filtered data may be copied to another range for subsequent analysis

�� Revert back to original data by choosing Data -> Filter -> Show All

The Advanced Filter can also be used to delete duplicate records in Microsoft Excel. For

this one needs to filter for unique records and then use the resulting rows to overwrite the

source cells. The entire procedure is summarized in the table given below:

1. In the list you want to filter, select the column or click a cell.

2. On the Data menu, point to Filter, and then click Advanced Filter.

3. In the Advanced Filter dialog box, click Copy to another location.

4. In the Copy to box, type a cell reference.

5. Select the Unique records only check box, and then click OK.

6. Select the data returned by the filter, and then click Cut on the toolbar.

7. Select the source data, and then click Paste on the toolbar.

5 Functions

5.1 Lookup Functions

The value of a cell can also be derived from (looked up from) a pre-defined list. In this

regard, it is important that the list to be looked up from should be in the same worksheet

and should be sorted. Consider creating a list of status codes applicable to an assessee.

The list of status codes and the description is entered in a separate area of the worksheet

(ideally the record section should be reasonably far from the data section – for easy

navigation, the record section may be appropriately named using a descriptive range

name.) On selection of an appropriate status code, Excel can look up the status

description from the list. There could be many instances where the lookup facility can be

put to practical use – referring the client particulars from the client database, etc. In this

regard, one may use the built-in functions of HLOOKUP or VLOOKUP or one may

choose to build the function through the use of the Lookup Wizard, an Add-in which

ships with MS-EXCEL. But to repeat, remember to sort the record section before you use

the lookup functions. (For sorting records, refer to Data -> Sort)

1. =VLOOKUP() can be used for columnar search and =HLOOKUP() can be used

for a row-wise search The arguments are:

�� The Lookup Value

�� The table range

�� The particular number of row or column in the table range

2. =INDEX() in its simplified version finds the intersection of a particular row and

column references. The arguments include: table range, row number & column

number. However, the row and column numbers can be made dynamic through

the use of =MATCH() command and this gives the functionality to the INDEX()

function. Such process is inbuilt in the Lookup Wizard

3. One can also build the function through the Lookup Wizard. Follow these simple

instructions:-

a. Select Tools -> Wizard -> Lookup

b. Follow the instructions in choosing the row, column and the range

c. To make the lookup dynamic, copy both the formula and lookup

parameters

5.2 Date Functions

EXCEL stores dates as numbers. (also known as date serial number) Conceptually a date

is stored as the number of days elapsed since 1st January 1900. To check this out, open a

blank sheet and type 1 in one of the cells. Format that number as a date (Format->Cells-

>Date). The resultant display is “01-01-00” which represents 1st January 1900. When a

date is directly entered into a cell, EXCEL automatically applies the date format and

stores the date serial number. Enter a date like 07-08-02 in one of the blank cells. Now

change the format of the cell as number (Format -> Cells -> Number). The display

changes to 37475. If it doesn’t the date is entered in text format. Check the display

orientation. Most probably, it will be left aligned!

How is this mode of internal storage of any relevance to us? It is, because it helps us

appreciate the limitations faced by EXCEL while manipulating dates. The first limitation

of EXCEL is that since dates are not stored as dates but as numbers, certain calculations

based on months and years have to be derived through formulae and cannot be in-built.

You would like to automatically calculate the rebate available for senior citizens based on

the date of birth. Let us say the date of birth is 17th March 1938 and we are interested in

knowing whether the person is senior citizen (age > 65 years) as on 31st March 2003. Let

us assume that the date of birth is entered in cell C3 and the year end date i.e. 31-03-2003

is entered in cell C2. I want to calculate the age. So I enter a formula +C2-C3 in cell C4.

To my dismay, I get a number 23755. What does this number represent? It represents the

number of days between C2 & C3. It is the age in days but I want the age in years. Can I

directly divide the answer by 365? Remember the calculations would be in-exact as there

would be leap years as well.

To move further, let us explore three important date functions YEAR (), MONTH () &

DAY (). The notations of these functions are self-explanatory and they are used to split a

date into its constituent components. For example, YEAR (“17-03-38”) will return 1938;

MONTH (“17-03-38”) will return 3 while DAY (“17-03-38”) will return 17. Armed with

these newly learned functions, I enter the formula +YEAR (C2)-YEAR (C3) in cell C4.

Voila! I get the answer as 65 and am delighted.

Note that the above formula is not fool-proof . Consider the date of birth to be 19th April

1938. While he had still not completed 65 years of age as on 31st March 2003, the above

formula treats him as a senior citizen. What was missing? I could make out that in the

transitory year, the above formula will not work as the months are not compared at all!

Using the IF function, the above formula can be modified as

+IF(MONTH(C2)>MONTH(C3),+YEAR(C2)-YEAR(C3),+YEAR(C2)-YEAR(C3)-1)

In effect, the above formula compares the month component of the date of birth to

determine whether the year has completed by the end of the previous year. If it has, it

simply calculates the difference in the year components else, it reduces the difference in

the year components by 1

In certain cases, one is interested in the difference in months (need not be completed

months). To calculate the number of months of delay, one uses the following formula:

+MONTH(C7)-MONTH(C2)+(YEAR(C7)-YEAR(C2))*12

The formula calculates the difference in months components of the dates. It also

considers the difference in the years components by taking the same into account and

multiplying the same by 12 to convert it into months.

Not too interested in using long and complicated formulae? If you have Analysis

Toolpack installed, there is a DATEDIF function which can do the job in a minute. So, to

calculate the completed years, I just enter the formula +DATEDIF(C3,C2,“y”). The “y”

refers to the completed years. Similarly, +DATEDIF(C2,C7,“m”) gives me the completed

months of delay which turns up to 13! But in certain cases, one would also like to include

partially completed months. In effect, one would like to advance the date to the end of the

month. This is where the EOMONTH() function is useful. So I modify my formula to say

+DATEDIF(C2,EOMONTH(C7,0),“m”). The answer is 14!

5.3 Numeric Functions

Various built-in functions can be used for manipulating numbers. A complete list of

functions is provided in Annexure “B”. Such functions can be used for rounding numbers

[ ROUND(), ROUNDDOWN(), ROUNDUP(), MROUND(), CEILING(), FLOOR() ] ,

counting the cells containing values [ COUNT(), COUNTA(), COUNTIF(),

COUNTBLANK() ] , identifying specific values within the list [ MAX(), MIN(),

LARGE(), SMALL() ] or converting the values into some other format [ ROMAN(),

TEXT() ] . The functions dealing with the totaling of numbers have already been covered

in detail earlier.

5.4 Text Functions

Text functions aim at either case conversion [UPPER(), LOWER(), PROPER()] ,

extraction of part of the text [LEFT(), RIGHT(), MID() ], identification and replacement

of particular alphabets within a text [ FIND(), SEARCH(), REPLACE(),

SUBSTITUTE()] or conversion into some other values [ VALUE(), DOLLAR() ]

5.5 Financial Functions

Function Description

PMT() Calculates the payment for a loan based on constant

payments and a constant interest rate.

PPMT() Returns the payment on the principal for a given period for

an investment based on periodic, constant payments and a

constant interest rate.

IPMT() Returns the interest payment for a given period for an

investment based on periodic, constant payments and a

constant interest rate

NPER() Returns the number of periods for an investment based on

periodic, constant payments and a constant interest rate

RATE() Returns the interest rate per period of an annuity.

PV() Returns the present value of an investment. The present

value is the total amount that a series of future payments is

worth now.

FV() Returns the future value of an investment based on

periodic, constant payments and a constant interest rate

NPV()

CUMIPMT() Returns the cumulative interest paid on a loan during a

particular period

CUMPRINC() Returns the cumulative principal paid on a loan during a

particular period

FVSCHEDULE() Returns the future value of an initial principal after

applying a series of compound interest rates.

NOMINAL() Returns the nominal annual interest rate, given the effective

rate and the number of compounding periods per year

EFFECT() Returns the effective annual interest rate, given the nominal

annual interest rate and the number of compounding

periods per year

ACCRINT() Returns the accrued interest for a security that pays

periodic interest

PRICE() Returns the price per $100 face value of a security that pays

periodic interest.

YIELD() Returns the yield on a security that pays periodic interest.

Use YIELD to calculate bond yield.

IRR() Returns the internal rate of return for a series of cash flows

represented by the numbers in values. These cash flows do

not have to be even, as they would be for an annuity.

However, the cash flows must occur at regular intervals,

such as monthly or annually.

XIRR() Returns the internal rate of return for a schedule of cash

flows that is not necessarily periodic.

5.6 Some more functions

In addition to the normal functions discussed above, there is a set of financial functions.

The same is dealt in a later module. Some more relevant functions are discussed below:

IF()

An IF function is made up of three parts: the condition, the true part, and the false part.

Select cell B6, type =IF(B2>10000,B2*D4,B2*E4) , and press Enter. The condition is

B2>10000; if true, the program will compute B2*D4, or if false the program will

compute B2*E4.

It is possible to replace one part of an IF statement with another IF statement; this is

called a nested IF. Select cell B6, edit the formula to read

=IF(B2>10000,B2*D4,IF(B8>4,B2*D4,B2*E4)) , and press Enter. This shows that if the

value in B2 is not greater than 10000, then a second condition, B8>4, will be considered.

It is also possible to combine conditions using logic functions like AND and OR.

Replace the formula in cell B6 with =IF(AND(B2>10000,B8>4),B2*D4,B2*E4). The

function AND shows that both conditions, B2>10000 and B8>4, must be met. Replacing

the AND with OR would result in either condition being met, the same accomplishment

as the nested IF.

CHOOSE()

The Choose function uses an index value to return a value from the list of values. It can

accommodate upto 29 alternative values

ISERROR()

The ISERROR function returns a True if a particular cell contains an error and can be

very useful in trapping errors and calculating further values based on the error position

CELL()

The CELL() function can be used to return useful information relating to a particular cell

or file.

6 The Look & Feel of Output

6.1 Formatting

6.1.1 Sheet

It is possible to add a picture to the background of the entire sheet. This should however

be done with caution.

6.1.2 Cells (or Range)

Various formatting features can be done on a single cell or a group of cells. To invoke the

formatting features, choose the Format Cells Command (Ctrl+1 / Right Click / Format ->

Cells). The following screen appears

The various tabs are analysed in the subsequent paragraphs

6.1.3 The Look of Data

This appears in the Numbers Tab The default tab is the Numbers tab. This is the one the

user will work with to format the type of number displayed. The options available

include: General, Number, Currency, Accounting, Date, Time, Percentage, Fraction,

Scientific, Text, Special, and Custom.

6.1.4 Alignment & Text Control

The text can be left aligned, centred or right aligned. It can even be rotated within a cell.

Often, a user wishes to have little more control over the text than is allowed within the

standard cell borders. Some available options are: Merge Cells which allows more than

one cell to be merged into one (accomplished by highlighting the ones the user wishes to

merge), Shrink to Fit which will reduce the apparent size of characters within selected

cells so that they will fit within the column and Wrap Text which wraps text into multiple

lines in a cell.

6.1.5 Fonts, Borders & Patterns

In order for grid lines (or any other formatting) to be present, the user must apply the

appropriate options. To apply borders right click on the active cell(s) then choose Format

Cells from the menu that appears. From the tabbed Formatting Window, left click on the

Borders tab to select it. There are parameter locations for the borders to be applied

top, bottom, left, right, etc.), as well as a list of line styles and a drop down menu of

color choices. The user can left click on the desired options. Left click the OK button to

apply the selections and continue.

6.1.6 Indented Text

In case one intends to indent the text within a particular cell, one can use the indent icons

on the standard toolbar.

6.1.7 Hiding Information

It is possible to hide entire sheets, rows or columns within a particular workbook. To hide

a sheet, Choose Format -> Sheet -> Hide. To hide a particular row or column, select the

row or column, right click and choose Hide. It is however not possible to hide the

contents of individual cells. The work-around solution is to format the cell contents to

display the same font color and cell background so that effectively the information gets

hidden.

6.2 Styles..

Styles represent standardized sets of formats. To initiate the styles, Choose the same from

the Format Menu. The following screen appears

One can choose from the existing styles or create a new one. The new style can be based

on an existing style. Since styles are workbook specific, one may need to use the merge

button to merge styles from existing workbooks. To create styles which are available

across all workbooks, create the same in the Personal.xls workbook

6.3 Conditional Formatting

Conditional formatting permits the user to apply special formatting settings that take

effect when the contents of the cell meet specified conditions. For instance, if there is a

loss under a particular head, you intend to colour it red so that it immediately catches

your attention. Similarly, you may like to colour your balance sheet totals to blue if they

do not tally. One very practical tip is to combine the ISERROR function with the

Conditional Formatting feature to hide errors. What is effectively done is that the font

and the background is set to the same color if the cell contains an error.

�� Select the range of cells for which the formatting is desired

�� Choose Format -> Conditional Formatting

�� Allows different forms of formatting based on the cell contents

�� Maximum of 3 different conditions can be specified

�� To suppress errors, choose Formula is =ISERROR() and then choose same colour

font as the background colour

6.4 Custom Views..

The Custom View feature is available from the View Menu. It ensures that one need not

set up the sheet each time one wants to print a particular sheet. The user first sets up the

entire sheet in the way desired for storage (including column & row widths, hidden rows,

autofilters, printer settings, etc.) He then initiates the Custom View Feature and allots a

descriptive name to the View. Later on, even if the print settings, etc. are altered, the user

can go back to the same view by selecting that specific view.

6.5 Printing

Before beginning the actual task of printing, it is necessary to orient the worksheet to the

specifics of a printer. This is done through the page setup command. The page setup

screen comes up which has four tabs: page (wherein paper size, orientation, compression

mode, etc. are specified), margins (to specify the margins on top, bottom, right, left),

header/footer (self explanatory) & sheet (which has some useful options – rows to repeat

at top, gridlines, etc.). One can also consider the use of Report Manager add-in which

permits multiple sheets or print areas to be synchronized as one print job (so as to

facilitate continuous page numbering) Additionally a Report Manager can work on

alternate views and scenarios within a single synchronised report.

6.6 Saying it with Charts..

It is said that an ounce of image is worth a pound of performance. A chart is a graphic

representation of worksheet data. Before understanding the creation of a chart, one needs

to be clear of the basic elements of a chart which include the X & Y Axes, X & Y Axis

Values, chart title, legend, data markers, tick marks, gridlines, data labels, etc.

To invoke charts Choose Chart from Insert Menu. The Chart Wizard takes you through

the rest of the process.

Excel provides for a wide variety of chart types. In case one is interested in depicting the

trend in a particular value, one should select a linear chart like Bar, Column, Line, etc. If

one is keen on looking at the constitution of various elements into a total, consider

Contribution charts like Stacked Charts, Pie, Doughnut, etc. Then there are specialized

charts like HLC Chart for analyzing stock trends, radar charts, scatter diagrams, etc.

7 Copying & Moving

One of the most common utilities of any Windows program is the cut/paste and the

copy/paste features. Needless to mention, the same are available in MS-EXCEL also. To

summarise, select a range of cells (it can be a set of non contiguous cells also), press

Ctrl+C to activate the Copy command from the keyboard after selecting the cells. Ctrl+X

is the keyboard command to cut the cells. You paste the cells from the keyboard by

pressing Ctrl+V. One can copy/move data across cells by using the mouse and the dragand-

drop technique. Simply drag-drop would imply a move, whereas holding the Control

key while dragging-dropping will imply a copy.

While copying values across poses no problems, one has to be careful while copying

formulae. When a formula containing a cell reference is entered into a cell, Excel keeps

track of that formula in two ways: one is relative referencing whereby the relative

position of the addressed cell and not the cell position itself is stored in the formula (this

is the default and is quite handy most of the times). For example, if A3 contains the

formula +A1+A2 and the same is copied to B3, the formula in B3 changes to +B1+B2.

While this is mostly beneficial, in some cases, one may want to freeze the cell position

referred and may not want the same to be changed in case of subsequent copying of data.

For this purpose, one needs to use the absolute referencing. Here, the exact cell position

of the addressed cell is stored in the formula. The absolute referencing is identified by the

use of the $ sign in the cell address. Thus $A$7 implies that the cell address A7 is

absolutely stored in the formula. One may also consider the use of mixed referencing

whereby either the row or the column remains constant. To make only the column or row

portion of a cell address absolute, press F4 key. Each time you press the F4 key, the $

moves to a different co-ordinate of the cell address. To summarise this issue, when you

copy a formula, relative addressing will change the cells that are referenced by the

formula. If you need any of the cells to remain constant, make sure that absolute

referencing has been added to the original formula before you copy it.

�� By default, Excel uses relative referencing.

�� To make either the column or the row referencing (or both) absolute, the column or

row number has to be preceded by a $ sign

�� The user can circle between the various options by using F4 Function key while in the

edit mode of the formula

7.1 Paste Special

Instead of copying entire cells, it is possible to copy specified contents from the cells —

for example, one can copy the resulting value of a formula without copying the formula

itself. To copy only partially a cell, follow these steps:

1. Select the cells you want to copy.

2. Click Copy.

3. Select the upper-left cell of the paste area.

4. On the Edit menu, click Paste Special.

5. Click an option under Paste, and then click OK.

– Various options to paste!

There are various options to paste special. The options are summarized in the screen-shot

below:

8 Saving Work & Protecting It

Once the sheet is prepared for data entry purposes which includes data validations,

lookups, conditional formatting, etc., one may like to ensure that none of such

validations/formulae are accidentally overwritten by the person entering the data. One

may therefore look at worksheet protection. To protect a particular sheet, choose Tools ->

Protection -> Sheet. One may provide a password if required. Similarly, to protect the

entire workbook, one chooses Tools -> Protection – Workbook. Once a sheet/book is

protected, no alterations are permitted in the sheet/workbook.

Many a times, the need may be to protect the sheet but at the same time permit data entry

in particular cells. To achieve such a dual purpose, one first unlocks the cells wherein the

data entry is to be permitted (Choose Format -> Cells -> Protection) and then follows up

the same with the sheet/workbook protection as outlined above. In such a scenario, entry

is permitted only into unlocked cells.

Worksheet protection still permits the viewing of the formulae. In many cases, the user

may not want the other person to know the formula. In that case, the cell formula can be

hidden (Choose Format -> Cells -> Protection). The contents of the cell are of course

displayed. It should be noted that hiding a cell has no effect unless the worksheet is itself

protected.

Protecting cells helps prevent accidental corruption of a spreadsheet. To protect cells:

1. All cells in a spreadsheet are automatically “locked” when the spreadsheet is

created. But this is inconsequential unless the sheet is protected.

2. Unlock only cells you may want to edit. To unlock a cell, select the cell, click

the right mouse button, select Format Cell (or choose Format/Cells), select the

Protection tab in the box that appears, click on the locked box to remove the

check that is there, this unlocks the cell.

3. To protect the spreadsheet, select Tools/Protection/Protect Sheet. In the

dialog box that appears, click OK. You may also apply a password but if you

forget it you cannot unprotect the sheet!

4. Once the sheet is protected, only unlocked cells can be edited.

8.1 File-Level Protection

One can password-protect the entire file. To do this, after creating the document, Choose

“Save As” from the File Menu. Select the general options from the Tools Tab and the

following screen appears:

In the file sharing options, specify the passwords. You can specify two types of

passwords, one authorising the user to open the file, another permitting him to modify the

same. In case you would just like to warn the user about the importance of the file

without introducing the hassles of passwords, you can select the “read-only

recommended” option.

9 Analysing Data

9.1 Data Tables

One may also consider the use of MS-EXCEL to perform what is commonly known as a

what-if analysis. What if analysis examines how sensitively a situation will react to

changes in factors that influence the situation. Let us take the example of a person

availing of a housing loan. The EMI payable would depend both on the interest rate and

the period of repayment (assuming that the loan amount is ascertained). Let us calculate

the EMI for a housing loan of Rs. 7.5 lakhs taken @ 11% per annum for a period of 15

years. I enter each of these basic data in separate cells A1 = 750000, A2 = 11%, A3 = 15

I enter the formula for calculation of EMI in Cell A4 as =PMT(A2/12,A3*12,-A1) {Note

that the EMI calculations in Excel are denominated in months and also that reverse cash

flows are indicated by negative numbers}. Now the person might be interested in

knowing the effect on the EMI for each change of 0.25% in the interest rate. Such a

sensitivity is known as what-if analysis. In Excel, what-if analysis is performed through

the use of data tables. A data table is a range of cells that shows the results of substituting

different values in one or more formulas. The Data Table command performs calculations

using a series of different input values and hence is an efficient alternative to creating

formulas in individual cells and editing or copying the formula when a value changes. To

initiate the process, choose the Table Command from the Data Menu.

A data-table can be either a one-variable table or a two variable table. In a one-variable

data table, the alternative values are entered as row labels and the resulting formulae are

specified as column labels. As such, it is possible to specify multiple formulae. Such a

table is known as column oriented data table. In case of a two variable table, the resulting

formula is entered at the intersection of the row and column labels (each of which

contains alternative values). As such, in case of two variable data table, one can specify

just one formula.

�� Useful for what-if analysis

�� Type the formulae in the columns & possible range of values in the rows

�� Select the range and Choose Data -> Table

�� Select the variable cell as the column input

�� For two variable data table, specify formula at the intersection of the row and column

9.2 Scenarios

The limitations of the data tables feature are but obvious! Time to introduce the Scenarios

feature. This feature enables you to analyse your data to see how changing one or more

values in a worksheet affects the other cells in the worksheet. Effectively using this

feature is a two step process: one is to create a scenario and the other step is to view the

results as a summary. The entire process is simple and self explanatory

�� What-if analysis on multiple criteria (pre-defined situations)

�� Choose Tools -> Scenario

1. Define a Scenario by “ADD”

2. Alter a Scenario by “DELETE” / “EDIT”

3. Concept of Changing Cells & Resultant Cells

�� View Results

�� Scenario Summaries

9.3 Goal Seek

Goal Seek is another useful feature which can be used to achieve a certain value in a cell

that contains a formula. The way this is done is to adjust the value of another cell that has

a direct effect on the original cell. After all, the valuation of closing stock has a direct

effect on the net profit!

�� Concept of working reverse way

�� Select Tools -> Goal Seek

9.4 Solver

Again, Goal Seek is an elementary function which may at times supply absurd results.

For example, it may let stocks be over-drawn. For a more sophisticated approach, choose

the Solver Add-in (cozily sitting on the Tools menu) which not only allows you to

specify constraints (so that stocks don’t get overdrawn or sales don’t exceed the

production capacity) but also permits multiple varying cells. The reports generated by the

add-in can help solve simple problems in linear programming.

�� Select Tools -> Solver

�� Concept of Target Cells, Changing Cells & Constraints

�� Utility of Answer Reports & Sensitivity Reports

�� Saving the solution as a scenario

10 PivotTables

PivotTable is a very powerful analysis tool built into MS-EXCEL. It helps in analyzing &

summarizing large collections of data. Such data can be derived from various sources.

The most common choice is to however create a pivot table from an Excel list. For the

purpose of understanding, the following Excel list consisting of time sheet records of a

professional firm is analysed using PivotTables

10.1 Creating a Pivot Table

For creating a PivotTable, choose the PivotTable command from the Data menu. The

PivotTable wizard appears and takes you through the process of creating a PivotTable

Step1 Specify the Data Source: Here we specify either an existing Excel list or an

external source of data. We also specify whether we want to create a PivotTable or a

PivotChart report. The default choices are generally Excel list and PivotTable. Choose

Next to specify the data range.

Step 2 Define the Data Range: Ensure that the correct range of cells has been included.

Click the next button to specify the location of the PivotTable

Step 3 Choose the location of the PivotTable. Select New worksheet and click Finish

10.2 Layout of the PivotTable

At this stage, it is necessary to understand certain terms relevant for the purposes of

PivotTables. For effective analysis, PivotTable uses the concepts of row & column fields

for summarizing and grouping data. The page field could be used to filter out the data on

a particular item. The data field contains the summary information. To create the

analysis, drag the desired item from the PivotTable Field list and drop it in the relevant

section of the main table.

10.3 Some Examples:

To obtain a report containing the gross amounts billed

for a particular client, drag the client field as row field

and “Bill Amount” field as the data field. The report is

ready!

On analyzing the report, I find that the firm earns

maximum revenues from Fast Limited.

Similarly, I could analyse the gross revenues earned by

a particular employee (remove the client field by

dragging it back to the pivottable field list and drag the

“resource name” field list to the row field area) or also get a report of segment-wise

revenue (drag the “work done” field to the row field area).

It is also possible to drill down to

the details of the above report by

clicking on a particular client and

choosing the field on which

detail is required (say resource

name) Further levels of data can

be selected by clicking

successive items. Similarly, it is

also possible to expand or

collapse the levels of data

displayed either by doubleclicking

or by choosing the

relevant command from the

PivotTable Toolbar. To view the

complete details of a particular

summarized amount, click on that amount to create a new sheet which displays only the

records that were included in that summarized amount.

Now suppose I want a cross dimensional analysis of data in terms of client-wise revenue

as well as segment-wise revenue. I position the client as row field and “work done” as the

column field. The data item of course continues to be gross amount. The resultant report

looks as under:

Now I divert my attention from the revenues generated to the time spent. I choose

“resource name” as the row field, “work done” as the column field and “time hours” as

the data field. I double click on the data field in the pivottable. A new screen pops up to

provide various options for displaying the data

The first list in the said screen (Summarize by) provides for alternative ways of

summarizing information. While the default is the sum of the data item, it is also possible

to choose either the average, maximum, minimum, number of occurrences, etc.

The second list in the said screen (Show data as) allows different methods of displaying

the summary data. I choose “% of row” and click OK to change the format of the chart.

The resulting chart helps me analyse the work specialities of specific employees.

Similarly, if I choose “% of column” Format for displaying data, I can analyse whether

the organization is dependent on a particular employee for a particular segment of work.

I could now replace the “work done” column field for the “client” column field and go

ahead to analyse the client-employee affiliations if any.

The possibilities are endless and the reports are displayed at the flash of a moment. The

only requirement for an effective analysis therefore is the quality of the data list

maintained.

11 Auditing Tools

11.1 Auditing Toolbar

Auditing is a means of finding errors and tracing the logic of a complex spreadsheet.

1. Select the cell you wish to audit.

2. Select Tools/Auditing

a. Trace Precedents shows what goes into the cells calculation

b. Trace Dependents shows where the audited cell is used

c. Trace Errors shows where an error statement arises

d. Remove all arrows removes the arrows when you are finished.

e. Show Auditing Toolbar is useful if you have a lot of auditing to do

The auditing tools can help in detecting
19th October 2006 From India , New Delhi

That is a very good listing of Excel posted by Deepak_ds_Sharma. I would like to add one feature of Excel. Go to C:\Program Files\Microsoft Office\OFFICE11. Open Office 11 and you will find a file named SOLVSAMP. This gives worked solutions on Linear programing Problems (Optimization, Tranportation, Assignment, Portfolio Management, etc.)
---------
Mayur
25th October 2006 From India , Ahmadabad
first of all i will like to thank you mayur for giving me some update regarding my knowledge.
and i checked it and i found that it is seriously very useful for linear programming problems.
regards
Deepak Sharma
25th October 2006 From India , New Delhi
This information is very useful and it’s also helpful with learning purpose.
6th July 2017 From India, Bhavnagar
 

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