## (solution) MM305 Unit 7 Project Name: Directions: The following software may

Even though independent gasoline stations have been having a difficult time, Susan Solomon has been thinking about starting her own independent gas station.  Susan?s problem is to decide how large her station should be.  The annual returns will depend on both the size of the station and a number of marketing factors related to oil industry and demand for gasoline.  After careful analysis, Susan developed the following table:

MM305 Unit 7 Project Name:

Directions: The following software may be used:

o Excel-&gt;Data Analysis

o Excel QM

o QM for Windows (PC only)

document. You may be required to also upload original files from Excel or QM for

Windows.

word for each question posed should be included.

Question 6 requires the use of the States Data File. The States Data file is located in

Be sure to put your name on this document and save it to your computer. Upload this

Word document as your Unit 7 submission in the course Drop Box. Submitting Your Project: Save your project in a location that you will remember and with your full name. When

you are ready to submit your project, click on the Dropbox and complete the steps below:

Click the link that says, ?Submit an Assignment.?

Make sure that you save a copy of your submitted project. 1 MM305 Unit 7 Project

1. Even though independent gasoline stations have been having a difficult time, Susan Solomon

has been thinking about starting her own independent gas station. Susan?s problem is to

decide how large her station should be. The annual returns will depend on both the size of

the station and a number of marketing factors related to oil industry and demand for gasoline.

After careful analysis, Susan developed the following table:

Size of Gasoline Station

Small

Medium

Large Good Market (\$)

\$1500

\$3500

\$7500 Fair Market (\$)

\$750

\$1500

\$4500 Poor Market (\$)

-\$500

-\$1000

-\$20,000 You may use Excel QM or QM for Windows:

1. What is the Maximax decision?

Explanation (include software output or calculation): 2. What is the Maximin decision?

Explanation (include software output or calculation): 3. What is the criterion of realism decision? Use ? = 0.4.

Explanation (include software output or calculation): 4. Develop an Opportunity Loss Table.

Table: 5. What is the Minimax Regret Decision?

Explanation (include software output or calculation): 2 MM305 Unit 7 Project

2. Data collected on the yearly demand for 50-pound bags of fertilizer at Sunshine Garden

Supply are shown in the following table. Year

1

2

3

4

5

6

7

8

9

10

11 Demand for Fertilizer

(1,000s of Bags)

15

13

12

10

9

9

12

14

10

15

12 You may use Excel QM to:

1. Develop a three-year moving average to forecast sales in year 12.

Explanation (include software output or calculation): 2. Develop a three-year weighted average to predict demand in year 12, in which sales in

the most recent year is given a weight of 4, the second most recent year is weighted 2

and sales in the third most recent year has a weight of 1.

Explanation (include software output or calculation): 3. Develop a regression/trend line to estimate the demand for fertilizer in year 12.

Explanation (include software output or calculation): 4. Analysis of the forecasting errors indicates which forecasting method (moving average,

weighted moving average or regression) is best in this situation?

Explanation: 3 MM305 Unit 7 Project

3. Kaplan College has decided to &quot;wire&quot; its campus. The first stage in this effort is to install the

&quot;backbone,&quot; i.e., to connect all the buildings. The table below gives the distances between the

various buildings on campus in hundreds of feet.

You may use QM for Windows or complete it by hand:

Distances in Hundreds of Feet

From

Building 1

Building 2

Building 3

Building 4

Building 5

Building 6 To

Building 1 Building 2

25 Building 3

22

18 Building 4

10

12

12 Building 5

12

9

23

20 Building 6

15

16

24

27

19 1. How should the buildings be connected to minimize the total length of cable?

Explanation (including any calculations or software output): 2. What length of cable is required? 4 MM305 Unit 7 Project

4. The following represents the distances in miles from a warehouse (node 1) to various cities in

Montana. The major outlet store is located at node 7.

From Node

1

1

2

2

3

3

3

4

4

5

5

6 To Node

2

4

3

4

4

5

6

5

7

6

7

7 Distance

500

250

200

120

50

75

350

500

200

245

375

400 You may use QM for Windows or complete it by hand:

1. Find the shortest route and distance from Node 1 to Node 7.

Answer: Explanation (including any calculations or software output): 5 MM305 Unit 7 Project

5. The network of a city sewer system and their capacities are shown below. Remember that the

arc has both capacity and reverse capacity. For example, row 1 is the flow from node 1 to

node 2 and row 2 is the reverse flow from node 2 to node 1. There are seven branches in this

network.

From

To Node Fluid Flow

Node

1

2

50

2

1

20

1

3

75

3

1

100

1

4

125

4

1

75

1

5

25

5

1

15

2

4

50

4

2

75

3

4

100

4

3

45

3

5

35

5

3

25

You may use QM for Windows or complete it by hand:

1. Determine the maximum flow (in hundreds of gallons of water per minute) from

node 1 to node 5.

Answer: Explanation (including any calculations or software output): 6 MM305 Unit 7 Project

6. The governor of Michigan believes that the state can improve the state?s poverty rate if the

state can reduce the college debt carried by its citizens and if they can reduce the percent of the

population not covered by health insurance. (This requires you to use the States Dataset file

that is included in Doc Sharing-&gt;Instructor Graded Projects.)

1. Using the States Data Set and Excel DataAnalysis (Regression), create the multiple

regression prediction equation of the form ? = 0 + 1(X1) + 2(X2)

Answer: Explanation (including any calculations or software output): 2. Predict the poverty rate for Michigan if the college debt was \$30,000 and the percent

not covered by insurance was 10% or 10?

Answer: Explanation (including any calculations or software output): 7 MM305 Unit 7 Project

7. A concessionaire for the local ballpark has developed a table of conditional values for the

various alternatives (stocking decisions) and states of nature (size of crowd).

Stocking Decision

Large Inventory

Average Inventory

Small Inventory Large Crowd (\$)

\$15,000

\$12,500

\$4,000 Average Crowd (\$)

\$12,000

\$25,000

\$3,000 Small Crowd (\$)

-\$1,000

\$7,500

\$2,500 You may use Excel QM or QM for Windows:

If the probabilities associated with the states of nature are 0.20 for a large crowd, 0.25 for an

average crowd, and 0.55 for a small crowd, determine:

1. The alternative that provides the greatest expected monetary value (EMV).

Answer: Explanation (including any calculations or software output): 2. The expected value of perfect information (EVPI).

Answer: Explanation (including any calculations or software output): 8

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