Introduction to Excel
Lecturer Notes
Nilgün Çokça
ECO319 Computer Applications and Data Analysis I
EXCEL FOR ECONOMICS
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
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.
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?
Our target is minimizing the cost and while minimizing it we have restricts.
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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
(2) =40*D1+60*D2
into C4
(3) =30*D1+15*D2
into C5
(4) =500*D1+600*D2
Z= in E1
into G1
D1 represents X; D2 represents Y.
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.
[3]
Adding Solver Commands to Data menu
Office button ~ Excel Options (in 2007)
File menu ~ Options (in 2010)
Select Add-Ins
[4]
Click to Go…
Click to Solver and then OK
[5]
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?
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 = 10𝑋11 15𝑋12 13𝑋13 8𝑋21 20𝑋22 11𝑋23 (𝑡𝑜𝑏𝑒𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒𝑑)
(𝑃𝑙𝑎𝑛𝑡 1 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦)
1𝑋11 +𝑋12 +𝑋13 ≤ 1.200
(𝑃𝑙𝑎𝑛𝑡 2 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦)
1𝑋21 +𝑋22 +𝑋23 ≤ 1.800
(𝑊𝑎𝑟𝑒ℎ𝑜𝑢𝑠𝑒 1 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦)
1𝑋11 +𝑋12 = 1.000
(𝑊𝑎𝑟𝑒ℎ𝑜𝑢𝑠𝑒 2 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦)
1𝑋12 +𝑋22 = 1.000
(𝑊𝑎𝑟𝑒ℎ𝑜𝑢𝑠𝑒 3 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦)
1𝑋31 +𝑋32 = 1.000
(𝑁𝑜𝑛 − 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑖𝑡𝑦𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡𝑠)
𝑋11 , 𝑋12 , 𝑋13 , 𝑋21 , 𝑋22 , 𝑋23 ≥ 0
[6]
[7]
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
Corn
Cost per acre
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?
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 ≤ 100
120𝑋 + 210𝑌 ≤ 15.000
110𝑋 + 30𝑌 ≤ 4.000
(110𝑥1,30)𝑋 + (30𝑥2)𝑌 → 𝑚𝑎𝑥.
[8]
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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+Y13 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.
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
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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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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.
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 →
4. X , Y ≥ 0
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½ Y –X ≤ 0
# of deluxe sold
: 20
# of standard sold
: 40
Profit
: 5600 $
[13]
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.
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
•
Their precinct
•
Age group
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•
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:
•
What is the party breakdown by precinct?
•
Do voters use permanent absentee ballots?
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•
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.
•
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.
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The Create PivotTable dialog appears.
•
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
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•
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
•
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
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•
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.
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
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case, I would drag the AGE GROUP column from the PivotTable Field List down below the
PRECINCT value in Row Labels.
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.
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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.
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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 crosstabulated against each of the other variables.
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