Part One Introduction to Excel October 2016 Written by N.Nilgün Çokça
Part One
Introduction to Excel
October 2016
Written by
N.Nilgün Çokça
EXCEL FOR ECONOMICS
CHAPTER ONE
INTRODUCTION TO MICROSOFT EXCEL
Introduction to Spreadsheets
A spreadsheet is the computerized equivalent of an accountant's ledger. As with the ledger, it
consists of a grid of rows and columns that enables you to organize data in a readily
understandable format.
"What is the big deal?" you might ask. The big deal is that after you change an entry (or entries),
the spreadsheet will, automatically and almost instantly, recomputed all of the formulas.
With a calculator and bottle of correction fluid or a good eraser, the same changes could also
be made to the ledger. But imagine for a moment a ledger with hundreds of entries, many of
which depend on the entry you wish to change. You can appreciate the time required to make
all the necessary changes to the ledger by hand. The same spreadsheet, with hundreds of entries,
will be recomputed automatically by the computer.
A worksheet is made up of columns and rows. The intersection of a column and a row forms a
block, or a cell. The border around the first cell on the worksheet tells you that this is the active
cell. This is the cell that will be affected by the next entry or command.
Each cell has a unique address, or reference. The cell reference of the active cell shows in the
Name box. The cell reference is A1 because the active cell is located in column A, row 1.
The mouse pointer has a plus-sign shape when it is in the worksheet area. The pointer changes
shape depending on its location and the action you are performing.
Row and Column Headings
A spreadsheet is divided into rows and columns, with each row and column assigned a heading.
Rows are given numeric headings ranging from 1 to 16.384 (the maximum number of rows
allowed). Columns are assigned alphabetic headings from column A to Z, then continue from
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AA to AZ and then from BA to BZ and so on, until the last of 256 columns (column IV) is
reached.
The intersection of a row and column forms a cell, with the number of cells in a spreadsheet
equal to the number of rows times the number of columns. Each cell has a unique cell reference;
for example, the cell at the intersection of column A and row 9 is known as cell A9. The column
heading always precedes the row heading in the cell reference.
Formulas and Constants
A constant is an entry that does not change; that is, it may be a number, such as a student’s
grade on an exam, or it may be descriptive text (a label), such as a student’s name. A formula
is a combination of numeric constants, cell references, arithmetic operators, and/or functions
that display the result of a calculation. Every cell in a spreadsheet contains either a formula or
a constant.
A formula always begins with an equal sign; a constant does not. Consider, for example, the
formula in cell E3, =(B3+C3+2*D3)/4, which computes Student’s semester average. The
formula is built in accordance which counts the final twice as much as either exam. Excel uses
symbols +, -, *, /, and ^ to indicate addition, subtraction, multiplication, division, and
exponentiation, respectively and follows the normal rules of arithmetic precedence.
INTRODUCTION TO MICROSOFT EXCEL
Microsoft Excel is a Windows application, and thus shares the common user interface with
which you are already familiar.
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Each window has its own Minimize, Maximize (or Restore), and Close buttons. Both windows
have been maximized and thus the title bars have been merged into a single title bar that appears
at the top of the application window. The title bar reflects the application (Microsoft Excel) as
well as the name of the workbook (Book1) on which you are working. A menu bar appears
immediately below the title bar. Two toolbars appear below the menu bar. Vertical and
horizontal scroll bars appear at the right and bottom of the document window.
The terminology is important, and we distinguish here between spreadsheet, worksheet, and
workbook. Excel refers to a spreadsheet as a worksheet. Spreadsheet is a generic term;
workbook and worksheet are unique to Excel. An Excel workbook contains one or more
worksheets.
The heavy border around cell E3 indicates that it (cell E3) is the active cell. Any entry made at
this time is made into the active cell, and any commands that are executed affect the contents
of the active cell. The active cell can be changed by clicking a different cell, or by using the
arrow keys to move to a different cell.
The displayed value in cell E3 is 88.0, but as indicated earlier, the cell contains a formula to
compute the semester average rather than the number itself. The contents of the active cell,
=(B3+C3+2*D3)/4, are displayed in the formula bar near the top of the worksheet. The cell
reference for the active cell appears in the Name Box at the left of the formula bar.
The Excel Workbook
An Excel workbook is the electronic equivalent of the three-ring binder. A workbook
contains one or more worksheet (or chart sheets), each of which is identified by a
tab at the bottom of the workbook. The worksheets in a workbook are normally
related to one another; for example, each worksheet may contain the sales for a
specific division within a company. The advantage of a workbook is that all of its
worksheets are stored in a single file, which is accessed as a unit.
The status bar at the bottom of the worksheet keeps you informed of what is happening as you
work within Excel. It displays information about a selected command or an operation in
progress. It also shows the status of the keyboard toggle switches, such as the Caps Lock key
or the Ins key, neither of which has been toggled on.
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Toolbars
Excel provides several different ways to accomplish the same task. Commands may be accessed
from a pull-down menu, from a shortcut menu (which is displayed by pointing to an object and
clicking the right mouse button), and/or through keyboard equivalents. Commands can also be
executed from one of many toolbars that appear immediately below the menu bar. The Standard
and Formatting toolbars are displayed by default.
The Standard toolbar contains buttons corresponding to the most basic commands in Excel-for
example, opening and closing a workbook, printing a workbook, and so on. The Formatting
toolbar appears under the Standard toolbar, and provides access to common formatting
operations such as boldface, italics, or underlining.
The toolbars may appear overwhelming at first, but there is absolutely no need to memorize
what the individual buttons do. That will come with time. Indeed, if you use another office
application such as Microsoft Word, you may already recognize many of the buttons on the
Standard and Formatting toolbars.
Entering Data
Data is entered into a worksheet by selecting a cell, then typing the constant or formula that is
to go into that cell. The entry is displayed in the formula bar at the top of the window as it is
being typed. The entry is completed by pressing the enter key, which moves the active cell
immediately below the current cell, or by pressing any of the arrow keys to move to the next
cell in the indicated direction. Pressing the right arrow key, for example, completes the entry
and moves the active cell to the next cell in the same row. You can also complete the entry by
clicking in a new cell, or by clicking the green check that appears to the left of the formula bar
as data is entered.
Save often.
A loss of power, whether it's your fault or the power company's can destroy a
creative masterpiece. The best insurance is to save your work constantly and, in
addition, to save your work whenever you are interrupted by a phone call, the
doorbell, etc.
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To replace an existing entry, select the cell by clicking in the cell, or by using the keyboard to
move to the cell. Type the corrected entry (as though you were entering it for the first time),
then complete the entry as described above.
MATHEMATICAL FUNCTIONS AND FORMULAS
Excel is NOT a statistics or econometrics software package it is a very powerful
spreadsheet program in which you can set up worksheets containing numbers and
formulas, create graphs and print the results.
In Excel when you want to write an equation you must start with “=” (equal to)
5+24 you must write 5+2^4
In mathematical form whether + or – sign would do the same. +A5-2^5
5^1/2 or 5^0,5 or SQRT(5)
The order of mathematical functions are:
( ) in side of parenthesis
- negative
% percentage
^ power
/,* division, multiplication
+, - sum, subtraction
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Examples:
1
=5+2*3^(1/2) 8,46
2
=(5^3-4^3)/(105+8^(1/3)) 0,57
3
=(3+5^0.5+1/(1+6^0.5))/(2+1/(1+3^0.5)) 2.335548
4
=(3+7^0,5+(12%-9^0,5)/6^3)/(8-4/(1+3^0,5)) 0,861766
5
=(8-(4/(3^0,5)))//(3-7^0,5+(12%-9^0,5)/6) -51,9748
Creating a Table of One Variable Function
y=x2 y=x3
x=1,2,3…….10 x2=? x3=?
Steps for creating a table of x2, x3.
Step 1. Click A1 and type X, in to B1 type X^2, into C1 type X^3.
Step 2. Write 1 to 10 in cells A3:A12 by using Edit/Fill/Series Command.
Edit/Fill/Series
Type 1 into A3 click Edit menu
select Fill/Series command
Select Column as Series in,
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Linear as Type,
Step Value: 1
Stop Value: 10
Click OK
Step 3. Click cell B2 and type =A2^2
Click cell C2 and type =A2^3
A2 must be empty.
Step 4. Highlight A2:C12 select Data menu Table command.
Click into Column input cell then click A2, then OK.
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Creating Table of Two Variables Function
x=1,2,3,...,5
Y=1,2,3,...,6
U(3,4)=? U(5,2)=? U(5,6)=?
U(x,y)= x / 2+y2
x=1,2,3……5 y=1,2,3……6
Steps for creating table of U(x,y):
Step 1. Write x variables into B1:F1, and y variables into A2:A7 by using Fill/Series command.
Step 2. Write formula x/2+y2 using Z1 for x, Z2 for y.
=Z1/(2+Z2^2) Z1 and Z2 are must be empty.
Step 3. Highlight A1:F7 select Data/Table.
Row input cell : Z1 as X
Column input Cell : Z2 as Y
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Then click OK.
C6 0,0740741 is for X=2 and Y=5 U(2,5)= 2/(2+5^2) 0,0740741
You can download Excel spreadsheet for these applications from the website. Excel_app_I.xlsx
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Matrix
The most general concept to introduce in the new algebra is that of a matrix of any dimensions.
A matrix is an ordered arrangement (not a single value) of a set of elements.
Definition: A matrix of order m x n is a set of m x n elements form the field F of real numbers,
arranged in rectangular from in m rows and n columns; it is denoted
𝐴 = [𝑎𝑟𝑠] [
𝑎11 𝑎12 ⋯ 𝑎1𝑛
𝑎21 𝑎22 ⋯ 𝑎2𝑛
⋮ ⋮ ⋯ ⋮𝑎𝑚1 𝑎𝑚2 ⋯ 𝑎𝑚𝑛
]
where r=1.2…….m denotes the rows and s=1.2……m the columns.
The order of the matrix, if not obvious, must always be specified and this can be done by giving
the range of values taken by r and s. the matrix is square when m=n and rectangular when mn;
in the latter case, m may be greater or less than n. There is no particular geometrical or
diagrammatic interpretation of a matrix and the terms “square” and “rectangular” are simply
convenient expressions of the “shape” of the block of elements concerned.
Among the numerous kinds of matrices, the following cases are of particular importance in
practice:
(i) Zero Matrix: 0 = [0] = [
0 0 ⋯ 00 0 ⋯ 0⋮ ⋮ ⋯ ⋮0 0 … 0
]
𝑚𝑥𝑛
of order m x n
All the elements are zero and, if their number is not obvious, it is necessary to specify.
(ii) Unit Matrix: this is a square matrix of any order n x n:
𝐼 = [𝛿𝑟𝑠] = [
1 0 ⋯ 00 1 ⋯ 0⋮ ⋮ ⋯ ⋮0 0 … 1
]
𝑟𝑥𝑠
(r, s= 1, 2, ….. n)
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The principal of I has entries 1; all other elements are 0. There is not just one unit matrix I; there
is such a matrix for each order n x n and the order must be understood or specified.
Matrix Sum
Cij=Aij+Bij i=1,2,3…….m
j=1,2,3……..n
2x32x3141210
864
864
235
BA
𝐴 + 𝐵 = 𝐶 = [9 9 10
14 18 22]
Select area for new matrix then type “=” highlight the area of matrix A, type “+”, highlight area
of matrix B.
Then to finish press Ctrl+Shift+Enter all together. You will get the result.
Data\Consolidate
Example: we have three electronic product A, B, C and we want to take the sum of three product
which sold in Ankara, İstanbul and İzmir in January, February and March.
Insert the number of sold products in matrix form.
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Highlight F8:H10, then Select Data menu Consolidate command.
. 𝐴𝑛𝑘𝑎𝑟𝑎 İ𝑠𝑡𝑎𝑛𝑏𝑢𝑙 İ𝑧𝑚𝑖𝑟𝐴 2200 4150 1700𝐵 1650 1800 1400𝐶 1050 2200 1100
Sum for function. Click into reference section and highlight the area of matrix A click add
button. And do the same steps for matrix B, and C. then click on OK button. You will see the
result:
Matrix Multiplication
A=[arp] is conformable with B=[bps] if A has as many column as B has rows:
A of order m x k and B of order k x n for any m and n. Then product AB is then the matrix
C=[crs] of order m x n, where crs is the inner product
k
p
psrpba1 .
i.e. C=AB implies bac ps
k
prprs
1
An alternative expression of the definition is in terms of inner products of vectors. If A is of
order m x k and B of order k x n, then the (r,s)th element in the product AB is the inner product
of the rth row of A, ar=(ar1,ar2, …..ark), with the sth column of B, bs=(b1s,a2s,…..bks). then
the rule of “across and down” or of “row and column” implies that vectors across A are taken
with vectors down B.
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In application of the definition, the first step is to check that the matrices to be multiplied are
indeed conformable. For example, matrices A and B of (3x2) and (2x2) respectively are
conformable and give a product AB of order (3x2). Put briefly: order (3x2) with order (2x2)
gives order (3x2). The second step is to apply the rule of “across and down”. The product AB
is obtained most easily by writing the definition in the form
[arp] x [bps] = [(
k
p
psrpba1
)]
Any one element of the product comes from a row of A matched off with a column of B; if the
element is the (r,s)th, then it comes from the rth row of A and the sth column of B. for example
02
10
22
02
10
10
01
12
AmxnxBnxk = Cmxk
The leading element in the product is the inner product formed from the first row (2,1) of A and
the first column (0, -2) of B:
2 x 0 + 1 x (-2) = -2
and similarly for the other elements.
22
23
2x3 58
64
53
564511
262312
x
x
CBA
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But we just write the matrix in Excel then select area for matrix C. Select Function command
from Insert Menu.
Select Math & Trig / MMULT for
matrix multiplication.
Type area of matrix A(B1:D2) in Array 1, and matrix B(B4:C6) in Array 2. Press OK.
Click once to end of formula
box. And press Ctrl+Shift+Enter all together.
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Matrix Transpose
A new process, not to be found in elementary algebra, can now be introduced into matrix
algebra. A given matrix of order mxn consists of mxn elements arranged differently, in n rows
and m columns, by simply interchanging the rows and columns. The result is a different matrix
of order nxm. It is called the transpose of the original matrix.
The transpose of a matrix A=[ars] of order mxn is the matrix A’= [asr] of order nxm.
The notation is simple; the addition of a prime to any matrix indicates transposition of rows and
columns, e.g. (AB)’ is the product matrix AB with rows and columns transposed.
642
531A ,
65
43
21'A
𝐴 = [2 5 83 2 6
]
Select area of transpose matrix (E1:G3) then type =TRANSPOSE(A1:C3) Ctrl+Shift+Enter.
𝐴𝑇 = [2 35 28 6
]
Inverse Matrix
The general form of a matrix, as considered so far, is rectangular its order is mxn where m is
generally not equal to n. In the present section, particular attention is paid to case m=n, to a
square matrix of order nxn.
If A=|A|=|ars| is the determinant obtained from A, then A is singular when A=0 and non-
singular when A0.
A-1 inverse of A: AA-1=A-1A=I
The matrices A and B must be square and A0.
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AAA
AAA
AAA
nnnn
n
n
rs
AA
AA
21
22212
12111'
1 1
(A0)
In Excel to take inverse matrix write matrix A
6512
386
195
A
in toA1:C3 then highlight area (B6:D8 ) for inverse matrix.
Insert /Function/ Math&Trig || Select MINVERSE
Select area of matrix A into Array.
Ctrl+Shift+Enter to see the result:
-0,158 0,1228 0,0877
A-1= 0,1805 -0,045 -0,053
-0,165 0,208 -0,035
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Linear Equations and Their Solution
[
𝑎11𝑥1+𝑎12𝑥2 + ⋯ + 𝑎1𝑛𝑥𝑛 = 𝑦1
𝑎21𝑥1+𝑎22𝑥2 + ⋯ + 𝑎2𝑛𝑥𝑛 = 𝑦2
⋮ ⋱ ⋮𝑎𝑚1𝑥1+𝑎𝑚2𝑥2 + ⋯ + 𝑎𝑚𝑛𝑥𝑛 = 𝑦𝑚
]
18
0
11
3425
25
321
322
321
xxxxxxxxx
to solve these equations we will write them in matrix form:
? X
18
0
11
b
3-14-
251
125
3
2
1
XXX
A
AX=b
A-1AX=A-1b
IX=A-1b
X= A-1b
Example 1.
4𝑥 + 3𝑧 + 5𝑡 = 25𝑥 − 𝑦 − 5𝑧 + 2𝑡 = −94𝑥 + 3𝑦 + 𝑡 = 37𝑥 + 2𝑦 + 9𝑡 = 14
} ?
Example2.
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5𝑥 + 𝑦 + 8𝑧 = 464𝑥 − 2𝑦 = 126𝑥 + 7𝑦 + 4𝑧 = 50
} ?
You can download Excel spreadsheet for these applications from the website.Excel_app_II.xlsx
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Equations with one unknown
y=x2-2x+1 to find x ‘s we must calculate a
acbb
2
42
In Excel to solve this equation we will take A1 as x; so
Click in C1 and type formula
=A1^2-2*A1+1
Give command Solver from Tools menu.
When you press Solve button you will see the root of the X in A1 and result of y in C1.
Nonlinear Equations
x2-y-1=0
3x-2y2-25=0
To solve these equations
click A1 and type formula =F1^2-F2-1
click A2 and type formula =3*F1-2*F2^2-25
by this typing F1 represents x, F2 represents y.
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Then select Solver from Tools menu
When you press Solve button you will see the result of equations. A1 equation 1; A2 equation
2, F1 x, F2 y.
Linear Programming
Consider the problem of nutrition in its economic aspects. A consumer buys a range of foods:
breads, meat, milk and so on. In determining his purchases, e.g. given prices on the market and
his income, his “preferences” for the various foods are taken into account, as in the usual theory
of consumer behavior. What are these “preferences”? In part, they are his tastes in food and his
habits in consumption. But, in part, they may also be an expression of his nutritional needs in
terms of calories, protein, vitamins and so on.
The problem is one of transformation: the foods bought at market prices are transformed into
intake of nutrients. There are two sides to the problem: the consumers’ diet is specified as to
aggregate content of calories, grams of protein, and so on; foods are then bought at given market
prices to minimize the cost of achieving the given nutritional content. The given technical data
of the problem consist of the specification of the nutrients in one unit of each food; this is a
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transformation function, here assumed can be achieved in all kinds of ways by buying foods in
various quantities. A feasible solution of the problem is any such set of purchases. The problem
is then resolved, and an optimum feasible solution obtained, if the set of purchases for smallest
cost is found.
Our target is minimizing the cost and while minimizing it we have restricts.
DK-1 X
BW-10 Y
Z=500X+600Y
40X+60Y 480 passenger X 0
30X+15Y 180 cargos Y 0
Steps for solving in Excel
(1) Type X= in C1 Y= in C2 Z= in E1
(2) =40*D1+60*D2 into C4
(3) =30*D1+15*D2 into C5
(4) =500*D1+600*D2 into G1
D1 represents X; D2 represents Y.
Example:
An airway firm has two different types of planes. DK-1 and BW-10. DK-1 can carry 40
passengers, 30 tons cargo. BW-10 can carry 60 passengers, 15 tons cargo.
Airway firm has signed an agreement to carry minimum 480 passengers and minimum of 180 tons
cargo for everyday. Fly cost for DK-1 is 500$ and for BW-10 is 600$.
For minimum total cost how many flight must be done with each plane?
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Select Solver from Tools menu.
See the results X=3 in D1
Y=6 in D2
Z=5100 in G1
Cost of DK-1 = 480 in C4
Cost of BW-10 = 180 in C5.
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Adding Solver Commands to Data menu
Office button ~ Excel Options (in 2007)
File menu ~ Options (in 2010)
Select Add-Ins
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Click to Go…
Click to Solver and then OK
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To solve this transportation problem as a LP model requires us to define the decision variables
to be the amount shipped from each plant to each location. It will be convenient to use a bit
different notation for this model; using subscripts to keep track of plants and warehouses Xi,J
will denote the amount shipped from Plant i to Warehouse j. For example:
X Plant1 to Warehouse1: X11 = Amount shipped from Plant1 to Warehouse1
X Plant2 to Warehouse3: X23 = Amount shipped from Plant2 to Warehouse3
This model requires six decision variables. In the following model, you see that the specification
becomes a bit tedious with so many variables. To make the formulation simpler we have not
listed all of the non-negativity constraints together on one line.
𝑍 = 10𝑋1115𝑋1213𝑋138𝑋2120𝑋2211𝑋23(𝑡𝑜𝑏𝑒𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒𝑑)
1𝑋11+𝑋12+𝑋13 ≤ 1.200 (𝑃𝑙𝑎𝑛𝑡 1 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦)
1𝑋21+𝑋22+𝑋23 ≤ 1.800 (𝑃𝑙𝑎𝑛𝑡 2 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦)
1𝑋11+𝑋12 ≤ 1.000 (𝑊𝑎𝑟𝑒ℎ𝑜𝑢𝑠𝑒 1 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦)
1𝑋12+𝑋22 ≤ 1.000 (𝑊𝑎𝑟𝑒ℎ𝑜𝑢𝑠𝑒 2 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦)
1𝑋31+𝑋32 ≤ 1.000 (𝑊𝑎𝑟𝑒ℎ𝑜𝑢𝑠𝑒 3 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦)
𝑋11, 𝑋12, 𝑋13, 𝑋21, 𝑋22, 𝑋23 ≥ 0 (𝑁𝑜𝑛 − 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑖𝑡𝑦𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡𝑠)
Example 1. Transporting Refrigerators
Suppose GE wishes to determine a shipping schedule to deliver 3000 side-by-side refrigerators
from two plants to three regional warehouses. The cost of shipping a refrigerator (via truck) from
each plant to each warehouse is given here:
To Warehouse
From Plant 1 2 3
1 10 15 13
2 8 20 11
Plant 1 can supply 1.200 of the total demand for refrigerators, and Plant 2 can supply 1.800. If
each of the three warehouses requires 1.000 refrigerators, what is the optimal shipping plan?
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X: # of acres of Corn
Y: # of acres of Wheat
P: Profit
X Y Constraints
Acres x y ≤100
Expenses 120x 210y ≤15.000
Yield 110x 30y ≤4.000
P 143x 60
Mathematical Form:
𝑋 + 𝑌 ≤ 100120𝑋 + 210𝑌 ≤ 15.000110𝑋 + 30𝑌 ≤ 4.000(110𝑥1,30)𝑋 + (30𝑥2)𝑌 → 𝑚𝑎𝑥.
Example 2.A farmer has 100 acres on which to plant two crops: corn and wheat. To
produce these crops, there are certain expenses, as shown in the table:
Item Cost per acre Item Cost per acre
Corn Wheat
Seed $ 12 Seed $ 40
Fertilizer $ 58 Fertilizer $ 80
Planting/care/harvesting $ 50 Planting/care/harvesting $ 90
Total $ 120 Total $ 210
After the harvest, the farmer must usually store the crops while awaiting favorable market
conditions. Each acre yields an average of 110 bushels of corn or 30 bushels of wheat. The
limitations of resources are
Available capital: $ 15.000
Available storage facilities: 4000 bushels
If the net harvest profit (after all expenses have been subtracted) per bushel of corn is $
1,30 and for wheat is $ 2,00, how should the farmer plant the 100 acres to maximize
profits?
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In formulating the LP model for this problem, some may have difficulty specifying the first
constraint. This constraint says that the sums of 42X and 30Y must at least equal 35(X+Y).
Thus, the first constraint can be written in either of the following two ways:
42X+30Y ≥ 35(X+Y) or
7X – 5Y ≥ 0
Constraints are:
X+Y ≥ 13
42X+30Y ≥ 35(X+Y) 7X – 5Y ≥ 0
Target:
Z = 60X+20Y Minimum Cost
Example 3.A company making animal feed uses two ingredients (X and Y) in one of their
best-selling products. A decision must be made regarding the amount of X and Y (measured
in tons) to include in the mix of this product to minimize total cost. Ingredient X costs the
company 60$ per ton, and ingredient Y costs 20$ per ton. The constraints on the mix each
day follow:
1. Company policy is that the mix must have an average of 35 units per ton of a nutritional
ingredient. Ingredient X provides 42 units per ton of this ingredient, whereas ingredient Y
provides 30 units per ton.
2. The company must make at least 13 tons each day: hence they consider X+Y13 to be
constraint.
A decision must be made regarding the amount of X and Y (measured in tons) to include in
the mix of this product to minimize total cost.
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#REF “Illegal Cell Reference”
The #REF! error occurs when you refer to a call that is not valid. The error is displayed
whenever Excel is unable to evaluate a formula because of an illegal cell reference. The most
common cause of the error is deleting the row, column, or all that contained the original cell
reference.
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X: Number of deluxe models sold
Y: Number of standard models sold
Z= $120X+$80Y
1. Hours: 2X+1Y ≤ 80
2. # Deluxe: X ≤ 30
3. Mix of deluxe and standard Policy: X ≥ 1/2Y X – ½ Y ≥ 0
4. X , Y ≥ 0
Example 4.Transco, Inc. makes a deluxe and a standard model of a Global positioning
System (GPS) –a handle device for navigating via a system of 24 Satellites. They are
currently trying to determine the optimal number of each model to produce each day. Their
profit is $ 120 for each deluxe model and $ 80 for each standard model.
Transco has 80 working-hours per day available (that is, 10 people working 8-hours shifts
per day) producing a deluxe model takes 2 hours, whereas producing a standard model
takes 1 hour.
No more than 30 deluxe models per day can be produced, and company policy is that the
number of deluxe models produced must be at least half of the number of standard models.
(For example, if 20 standard models are produced, the number of deluxe models must be
at least 10.) The company can sell all of the GPS models it produces.
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# of deluxe sold : 20
# of standard sold : 40
Profit : 5600 $
You can download Excel spreadsheet for these applications from the
website.Excel_app_III.xlsx
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Pivot Tables
A pivot table extends the capability of individual database functions by presenting the data in
summary form. It divides the records in a list into categories, then computes summary statistics
for those categories.
A pivot table is created by using the Pivot Table Wizard, which prompts you for the information
to develop the pivot table. You indicate the field names for the row and column labels. You
also indicate the field on which the computation is to be based and means of computation. The
Pivot Table Wizard does the rest. It creates the pivot table in its own worksheet within the same
Workbook as the list on which it is based.
Pivot tables provide the almost in flexibility, in that you can vary the row or column categories
and/or the way the statistics are computed. The pivot table dialog box shows just how easy it is
to create a pivot table. The field names within the associated list appear at the right of the dialog
box. To create the pivot table, you simply drag a field name(s) to the row, column, or data areas
of the table. Click the Next command button to supply the finishing touches to the pivot table,
after which the pivot table will appear in its own worksheet.
Once a pivot table has been created, you can easily add or remove categories by dragging the
field names on or off the table within the PivotTable Wizard. You can also switch the orientation
(pivot the table) by dragging a field to or from the row or column area. And finally, you can
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modify the worksheet on which the pivot table is based then refresh the pivot table to reflect
the changes made to the worksheet.
Cross-Tabulation:
Suppose you have been looking at a university department’s web page which lists staff
alphabetically by name, and gives an indication of their position in the department ( showing
who is a Professor, a senior lecturer or ordinary lecturer). You notice that of the twenty staff
listed six are women, but only one of the four Professors is a woman. You decide to investigate
the relationship between position and gender more systematically.
You enter the person’s name, gender and position into a spreadsheet as shown in Figure
What you need to do is to draw up a table, known as a contingency table, which has two columns
to distinguish the gender of the individuals and three rows to distinguish the staff according to
their position or status.
The table would show the number of cases falling into each two-way category. Now with a
small data set such as we have here it is easy enough just to count up the cases manually.
Excel steps for count up gender and position for staffs.
Select through B1:C21 then Data menu Pivot Table wizard.
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Put Gender to column and Position to row, and again Position to data. E1, an area of the
worksheet where you would like the table to appear.
You can also download sample spreadsheet to try these methods yourself.
(CrossTabulation.xlsx)
What is a Pivot Table?
Pivot tables are an Excel feature that you should learn how to use. Instead of analyzing rows
upon rows of records, a pivot table can aggregate your data and show a new perspective and
few clicks. You can also move columns to rows or vice versa. The problem is people believe
creating a pivot table is too difficult to learn.
You might think of a pivot table as a user created summary table of your original spreadsheet.
You create the table by defining which fields to view and how the data should be displayed.
Based on your field selections, Excel aggregates and organizes the data so you see a different
view of your data.
As example, I’ve uploaded a sample spreadsheet of 4000 fictitious voters, which includes the
following data fields:
Voter ID
Party Affiliation
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Their precinct
Age group
When they last voted
Years they’ve been registered
Ballot status
Looking at the first 20 data records, you can see the data is boring. It’s enough to make you roll
your eyes and fall asleep. In this format, the key question it answers is how many voters exist
in all the precincts.
Using Excel pivot tables, you can organize and group the same data in ways that start to answer
questions such as:
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What is the party breakdown by precinct?
Do voters use permanent absentee ballots?
Which precincts have the most Democrats?
How many voter pamphlets do I need for Precinct 2416?
Do 18-21 year olds vote?
A pivot tables allow you to group the spreadsheet or external data source by any of your data
fields. The thumbnail below shows a count of voters by party by precinct.
Using a pivot table, I can continue to slice the data by selecting additional fields from the
PivotTable Field List. For example, I can take the same data and segment by voter age group.
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Understanding the Pivot Table Structure
In the thumbnail above, I’ve labeled the main areas of the pivot table.
1. PivotTable Field List – this section in the top right displays the fields in your
spreadsheet. You may check a field or drag it to a quadrant in the lower portion.
2. The lower right quadrants - this area defines where and how the data shows on your
pivot table. You can have a field show in either a column or row. You may also indicate
if the data should be counted, summed, averaged, filtered and so on.
3. The red outlined area to the left is the result of your selections from (1) and (2). You’ll
see that the only difference I made in the last pivot table was to drag the AGE GROUP
field underneath the PRECINCT field in the Row Labels quadrant.
How to Create a Pivot Table
There are several ways to build a pivot table. Excel has logic that knows the field type and will
try to place it in the correct row or column if you check the box. For example, data that is
numeric such as Precinct counts tends to appear to the right in columns. Data, which is textual,
such as Party would appear in rows.
While you can simply check fields to display and let Excel build your pivot table, I prefer to
use the “drag and drop” method. This is partly because I like to visualize my data in columns
and rows. I think it may also be easier if you have fields, which can appear to be numbers like
a precinct value.
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Open your original spreadsheet and remove any blank rows or columns.
Make sure each column has a heading, as it will be carried over to the Field List.
Make sure your cells are properly formatted for their data type.
Highlight your data range, Click the Insert tab.
Select the PivotTable button from the Tables group.
Select PivotTable from the list.
The Create PivotTable dialog appears.
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Double-check your Table/Range: value.
Select the radio button for New Worksheet.
Click OK.
A new worksheet opens with a blank pivot table. You’ll see that the fields from our source
spreadsheet were carried over to the PivotTable Field List
Drag an item such as PRECINCT from the PivotTable Field List down to the Row
Labels quadrant. The left side of your Excel spreadsheet should show a row for each
precinct value. You should also see a checkmark appear next to PRECINCT
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The next step is to ask what you would like to know about each precinct. I’ll drag the
PARTY field from the PivotTable Field List to the Column Labels quadrant. This will
provide an additional column for each party. Note that you won’t see any numerical data
To see the count for each party, I need to drag the same field to the Values quadrant. In
this case, Excel determines I want a Count of PARTY. I could double-click the entry
and choose another Field Setting. Excel has also added Grand Totals.
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As you build your pivot table, you’ll probably think of additional ways to group the information.
For example, you might want to know the Age Range of voters by Precinct by Party. In this
case, I would drag the AGE GROUP column from the PivotTable Field List down below the
PRECINCT value in Row Labels.
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Each age group is broken out and indented by precinct. At this stage, you might also be thinking
of usability. As with a regular spreadsheet, you may manipulate the fields. For example, you
might want to rename “Grand Total” to “Total” or even collapse the age values for one or more
precincts. You can also hide or show rows and columns. These features work the same way as
a regular spreadsheet.
One area that is different is the pivot table has its own options. You can access these options by
right-clicking a cell within and selecting PivotTable Options… For example, you might only
want Grand Totals for columns and not rows.
There are also ways to filter the data using the controls next to Row Labels or Column labels
on the pivot table. You may also drag fields to the Report Filter quadrant.
Troubleshooting Pivot Tables
You might encounter several “gotchas” with this example file or another spreadsheet.
Sometimes when you move around your pivot table the PivotTable Field List disappears. To
get it back, click any cell with a value.
You can also move or “pivot” your data by right clicking a data field on the table and selecting
the “Move” menu. From here, you can move a column to a row or even change the position.
An example of this might be the values for “LAST VOTED” since Excel will sort by the month
first. You might prefer to move the data so the election dates are in a chronological order.
Pivot tables may not make the election data exciting, but it can make the analysis process easier.
Without these tables, you’d probably spend more time filtering, sorting and subtotaling. The
other benefit is that it’s easy to start over by deselecting fields or moving them to another
location. Feel free to download the tutorial spreadsheet below and play with the data. This will
probably be the only time you’re allowed to manipulate election data.
You can also download sample spreadsheet to try these methods yourself.
(PivotTableExample.xlsx)
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An Example for Pivot Table
Staffs in a company have been sent a questionnaire asking them whether or not have received
any IT training. The questionnaire also asks respondents to indicate their gender, status in the
company (junior or senior) and their employment mode (Full-time or Part-time). The results for
one branch are shown in the table below:
Use PivotTable Wizard to produce contingency tables showing IT training responses cross-
tabulated against each of the other variables.
You can also download sample spreadsheet to try these methods yourself. (ITtraining.xlsx)