Unit 7 Project

 

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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

Good Market ($)

Fair Market ($)

Poor Market ($)

Small

$5,000

$2500

-$1000

Medium

$10,000

$7000

-$5,000

Large

$25,000

$12,500

-$20,000

 

 

 

You may use Excel QM or QM for Windows:

 

 

 

  1. What is the Maximax decision?

    Answer:

     

    Explanation (include software output or calculation): 

     

     

  2. What is the Maximin decision?

    Answer:

     

    Explanation (include software output or calculation): 

     

     

     

  3. What is the criterion of realism decision? Use α = 0.25.

    Answer:

     

    Explanation (include software output or calculation): 

     

     

     

  4. Develop an Opportunity Loss Table.

    Table:

 

 

 

 

 

  1. What is the Minimax Regret Decision?

    Answer:

     

    Explanation (include software output or calculation): 


 

 

2. Data collected on the yearly demand for 50-pound bags of fertilizer at Sunshine Garden Supply are shown in the following table.

 

 

 

Year

Demand for Fertilizer (1,000s of Bags)

1

3

2

4

3

6

4

8

5

6

6

7

7

8

8

7

9

9

10

6

11

5

 

 

 

You may use Excel QM to:

 

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

 

Answer:

 

Explanation (include software output or calculation):

 

 

 

 

 

  1. Develop a 3-year weighted average to predict demand in year 12, in which sales in the most recent year is given a weight of 1, the second most recent year is weighted 2 and sales in the third most recent year has a weight of 3.

 

Answer:

 

Explanation (include software output or calculation):

 

 

 

 

 

  1. Develop a regression/trend analysis to estimate the demand for fertilizer in year 12.

 

Answer:

 

Explanation (include software output or calculation):

 

 

 

 

 

  1. Analysis of the forecasting errors indicates which forecasting method (moving average, weighted moving average or regression) is best in this situation?

    Answer:

 

Explanation:


 

 

3. Kaplan College has decided to “wire” its campus. The first stage in this effort is to install the “backbone,” 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

To

 

 

 

 

 

 

Building 1

Building 2

Building 3

Building 4

Building 5

Building 6

Building 1

 

15

12

10

14

9

Building 2

 

 

8

2

5

6

Building 3

 

 

 

16

13

14

Building 4

 

 

 

 

6

7

Building 5

 

 

 

 

 

8

Building 6

 

 

 

 

 

 

 

 

 

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

 

Answer:  

 

Explanation (including any calculations or software output):

 

 

 

 

 

  1. What length of cable is required?

     


 

 

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

To Node

Distance

1

2

75

1

4

375

2

3

200

2

4

250

3

4

450

3

5

25

3

6

175

4

5

50

4

7

350

5

6

145

5

7

275

6

7

450

 

 

 

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. 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 Node

To Node

Fluid Flow

1

2

250

2

1

200

1

3

150

3

1

225

1

4

325

4

1

150

1

5

300

5

1

125

2

4

375

4

2

225

3

4

250

4

3

100

3

5

175

5

3

400

 

 

 

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. The governor of Michigan believes that the state can improve the state’s crime rate if the state can reduce the percent of the population not covered by health insurance and reduce the percentage of teen pregnancy. (This requires you to use the States Dataset file that is included in Doc Sharing->Instructor Graded Projects.)

 

 

 

  1. Using the States Data Set and Excel DataAnalysis (Regression),create the multiple regression prediction equation of the form Ŷ = b0 + b1(X1) + b2(X2)

 

Answer:  

 

 

 

Explanation (including any calculations or software output):

 

 

 

  1. Predict the crime rate for Michigan if the percent not covered by insurance was 25% or 25 and the percent of teen pregnancy was 10% or 10?

 

Answer:  

 

 

 

Explanation (including any calculations or software output):

 

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 Crowd ($)

Average Crowd ($)

Small Crowd ($)

Large Inventory

$15,000

$10,000

$5,000

Average Inventory

$12,500

$1,000

$5,500

Small Inventory

$8,000

$3,000

$1,000

 

 

 

You may use Excel QM or QM for Windows:

 

 

 

If the probabilities associated with the states of nature are 0.3 for a large crowd, 0.3 for an average crowd, and 0.4 for a small crowd, determine:

 

 

 

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

 

 

 

Answer:  

 

 

 

Explanation (including any calculations or software output):

 

 

 

 

 

  1. The expected value of perfect information (EVPI).

 

 

 

Answer:  

 

 

 

Explanation (including any calculations or software output):

 

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