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

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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?

Answer: The Maximax decision would be to choose to build the large station for \$170k with the

maximum annual returns based on a good market.

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

Answer: The Maximim decision would be to choose to build the small station as the loss is the

least at \$30k

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

Answer: 2 MM305 Unit 7 Project

The weighted decision of a = 0.4 would be to choose to build the small station as the

\$126k shows the greatest possible gains could be made

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

Table: 5. What is the Minimax Regret Decision?

Answer: How much I would leave on the table if I made that decision.

Explanation (include software output or calculation): 3 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.

Answer: 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: 4 MM305 Unit 7 Project 5 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?

Answer: So a 9 cable would connect building 2 and 5. Buildings 4 and 1 would be connected by a 10

cable. Thus Buildings 1 and 5 and 4 and 3 could connected by a 12 cable each. Leaving

Building 1 and 6 to be connected by a 15 cable. Total hundreds of feet would include

9x10x12x12x15=194,400

Explanation (including any calculations or software output): 2. What length of cable is required? 194,400 6 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): 7 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.

Explanation (including any calculations or software output): 8 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: We then create a new variable in cells C2:C6, cubed household size as a regressor.

Then in cell ... The population regression model is: y = ?1 + ?2 x2 + ?3 x3 + u ...

R2 = 1 - Residual SS / Total SS (general formula for R2)

Run regression replace B1 with numbers states

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: We then create a new variable in cells C2:C6, cubed household size as a regressor.

Then in cell ... The population regression model is: y = ?1 + ?2 x2 + ?3 x3 + u ...

R2 = 1 - Residual SS / Total SS (general formula for R2) Explanation (including any calculations or software output): 9 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:

Answer: The alternative that provides the greatest expected monetary value (EMV). Explanation (including any calculations or software output): 1. The expected value of perfect information (EVPI). EMV ..20 x the amount in each inventory 15k x .2 15k x .25 add up max is the answer

Answer: maximum EMV = \$12,200 EVPI 2. The expected value of perfect information (EVPI). = 1380012200 = 1,600 Explanation (including any calculations or software output):

8. Allen Machines specializes in developing weed-harvesting equipment that is used to clear

small lakes of weeds. Allen Machines is contemplating the construction of a machine that

would harvest weeds on narrow rivers and waterways. The activities and time in weeks

necessary to build one of these experimental machines are shown in the table below.

Activity

A

B

C

D

E Immediate Predecessors

none

A

B

A

A Time in Weeks

4

3

2

4

2 10 MM305 Unit 7 Project

F

G

H E

B, C

D,F 2

2

1 1. What is the minimum possible time required for completing the project?

2. What is the latest possible time that Activity E may be started without delaying the

completion of the project?

3. What is the latest finish time for Activity H?

4. What is/are the critical path(s)?

Explanation: (Please include Gantt Chart and/or Network Graph): 11 MM305 Unit 7 Project

9. The following is the activity and associated costs for the renovation of the local high school

football stadium. The times are in weeks.

Explanation: You can enter the above information into QM for Windows-&gt;Project

Management-&gt;Cost Budgeting. Activity

A

B

C

D

E

F

G

H Immediate Predecessor

A

B

B

C, D

C, D

E, F Time

8

4

6

2

3

7

5

1 Cost (\$)

20,000

12,000

15,000

15,000

10,000

50,000

35,000

1,000 1. What is the critical path and total time required for this project?

Explanation: (include Gantt Chart and/or Network Graph): 2. How much of the total (cumulative) budget would be spent in Week 8 (Period 8) with the

earliest start budget?

Answer: Explanation (include cost budgeting table): 12 MM305 Unit 7 Project

10. Precision Manufacturing has a government contract to produce stainless steel rods for use

in military aircrafts. Each rod is required to be 35 millimeters in diameter. Each hour, random

samples of size n = 5 rods are measured to check process control. Four hours of

observations yielded the following:

Explanation: You are looking at the control limits for the variable, average diameter. You can

use Excel QM or QM for Windows-&gt;Quality Control-&gt;x-bar and r-charts. Time

9 A.M.

10 A.M.

11 A.M.

Noon Rod 1

34.5

35.1

38.9

25 Rod 2

34.9

34.7

35

35.2 Diameter

Rod 3

37.9

33

37.9

32.1 Rod 4

36

35.4

38.3

38.1 Rod 5

35.9

34.9

36.5

35 1. Construct the xbar-chart and the R-chart.

Please include charts below: 2. Is the process in control? xbar chart UCL = R-chart UCL = xbar chart LCL = R-chart LCL = Explanation: 13 MM305 Unit 7 Project

11. Modern Electronics specializes in manufacturing modern electronic components. It also

builds the equipment that produces the components. Modern Electronics is considering building

a new facility but the estimated profits would be impacted by the type of market that develops.

The probability for a strong market is 0.3; for a fair market is 0.3; and for a poor market is 0.4.

You are responsible for advising the president of Modern Electronics on the type facility that

should be built or to not build a facility at all. The table shows the estimated profits under each

market and for each size facility.

Explanation: You can use QM for Windows-&gt;Decision Analysis-&gt;Decision Table with the above

information.

Strong Market Estimated Profits

Fair Market Poor Market Build a large facility 30,000 25,000 -20,000 Build a medium-size facility 27,500 25,000 -10,000 Build a small facility 15,000 12,500 -1000 Do not build a facility 0 0 0 1. What is your recommendation to the president based on expected value that maximizes

profits (EMV).

Explanation (include expected monetary value):

Software Output: 2. Provide a second recommendation to the president that minimizes regret.

Explanation (include expected monetary value):

Software Output: 14 MM305 Unit 7 Project

12. Consulting income at Kaplan Associates for the period February ? July is shown in the table

below. Assume that the initial forecast for February is \$90,000. Use Exponential

smoothing to forecast August?s income.

Explanation: You can use Excel QM?Forecasting?Exponential with the above information. Month

February

March

April

May

June

July Income (\$1,000)

90.0

88.5

74.8

91.7

91.3

92.8 1. Use a smoothing constant of ? = 0.1.

Answer: Explanation (include software output): 2. Use a smoothing constant of ? = 0.6.

Answer: Explanation (include software output): 3. Analysis of the forecasting errors indicates which forecasting constant is best in this

situation?

Answer: Explanation: 15 MM305 Unit 7 Project

13. Johnson Construction Company is in the process of installing power lines to a large housing

development. The company wants to minimize the total length of wire used, which would

minimize the company?s cost. The housing development is shown below. Each house has

been numbered, and the distances between houses are given in hundreds of feet.

Explanation: We want to create the minimum spanning tree (MST) for this network since all

houses need to be connected. You can use QM for Windows to do this. 1. What do you recommend to Johnson Construction Company?

Answer: Explanation (including software output): 16 MM305 Unit 7 Project

14. The storm drains in the Cedar Rapids, Iowa, have been upgraded following the devastating

floods of 2008. The network of storm drains and the capacities are shown below. Determine

the maximum flow (in hundreds of gallons of water per minute) from node 1 to node 5.

Remember that the arc has both capacity and reverse capacity.

Explanation: You can use QM for Windows?Networks?Maximal Flow with the above

information. From

Node

1

2

1

3

1

4

1

5

2

4

3

4

3

5

4

5 To Node Fluid Flow 2

1

3

1

4

1

5

1

4

2

4

3

5

3

5

4 125

100

250

100

250

450

200

75

100

300

150

250

190

400

50

Explanation (include software output): 17 MM305 Unit 7 Project

15. From the States Data Set the following output for College and for the Bachelors was

created. 1. Which variable has the greatest relative variation?

Answer: Explanation (including calculations): 18 MM305 Unit 7 Project

16. You are a consultant working for Kaplan Consulting. The U.S. Department of Labor has

requested assistance in evaluating the impact of economic stimulus on the unemployment

rate. From the States Data Set the following t test was conducted to answer the question:

?Has there been a significant reduction in the national unemployment rate between

January and March??

Output from PhStat2: Output from Excel-DataAnalysis: 1. What is the Null and the Alternative Hypotheses?

Ho:

Ha:

2. What is your level of alpha (?)? 3. What is your decision about the hypothesis based on the software output?

4. Has there been a significant reduction in the national unemployment rate between

January and February? 19 MM305 Unit 7 Project

17. The Governor of a southern state has asked Kaplan Consulting to determine if the state

were able to increase the percentage of its population with a Bachelor?s Degree to 45%, what

might be the expected median household income based on 2000 data? Here is the output from

the Regression procedure from Excel. 1. What would be the predicted median household income if the percentage of the

population in the state were 45% or 45?

Explanation (include all calculations): 20

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