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The Rent-A-Dent car rental company allows its customers to pick-(Answered)

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Question

The Rent-A-Dent car rental company allows its customers to pick up a rental at one location and return it to any of its other locations.? Currently, two locations (1 and 2) have 16 and 18 surplus cars, respectively, and four locations (3, 4, 5 and 6) each need 10 cars.? The costs of getting the surplus cars from locations 1 and 2 to the other locations are shown in the table below.

Costs of Transporting Cars Between Locations

Location 3

Location 4

Location 5

Location 6

Location 1

54

17

23

30

Location 2

24

18

19

31

Because 34 surplus cars are available at locations 1 and 2, and 40 cars are needed at the other locations, some locations will not receive as many cars as they need.? However, management wants to make sure that all the surplus cars are sent where they are needed and each location needing cars receives at least five. The company wants to determine the lowest cost plan for meeting their objectives.? They have created a network model in the accompanying spreadsheet (see tab ?Rent-A-Dent?), including defining all of the solver inputs.? You can assume that their formulation is all correct.? Using their file, create a sensitivity report and answer the questions in the Rent-A-Dent sheet.? (Do not redo the formulation to answer the questions, or use the SolverTable add-in.)? In addition to answering the questions, indicate on your sensitivity report the numbers that you are using to answer the questions.


Microsoft Excel 15.20 Sensitivity Report

 

Worksheet: [u1019851 (Autosaved).xlsx]Rent-A-Dent

 

Report Created: 4/30/2016 8:33:03 PM

 


 

Variable Cells

 

Cell

 

$D$2

 

$D$3

 

$D$4

 

$D$5

 

$D$6

 

$D$7

 

$D$8

 

$D$9

 


 

Name

 

Flow

 

Flow

 

Flow

 

Flow

 

Flow

 

Flow

 

Flow

 

Flow

 


 

Final Reduced Objective Allowable Allowable

 

Value

 

Cost

 

Coefficient Increase Decrease

 

0

 

26

 

54 1.00E+030

 

26

 

10

 

0

 

17

 

5 1.00E+030

 

1

 

0

 

23

 

2

 

5

 

5

 

0

 

30

 

5

 

2

 

9

 

0

 

24

 

2

 

5

 

0

 

5

 

18 1.00E+030

 

5

 

9

 

0

 

19

 

5

 

2

 

0

 

5

 

31 1.00E+030

 

5

 


 

Constraints

 

Cell

 

$G$2

 

$G$3

 

$G$6

 

$G$7

 

$G$8

 

$G$9

 

$G$6

 

$G$7

 

$G$8

 

$G$9

 


 

Name

 

Flow Out

 

Flow Out

 

Flow In

 

Flow In

 

Flow In

 

Flow In

 

Flow In

 

Flow In

 

Flow In

 

Flow In

 


 

Final Shadow Constraint Allowable Allowable

 

Value

 

Price

 

R.H. Side Increase Decrease

 

16

 

28

 

16

 

1

 

1

 

18

 

24

 

18

 

1

 

4

 

9

 

0

 

10 1.00E+030

 

1

 

10

 

-11

 

10

 

1

 

1

 

10

 

-5

 

10

 

4

 

1

 

5

 

0

 

10 1.00E+030

 

5

 

9

 

0

 

5

 

4 1.00E+030

 

10

 

0

 

5

 

5 1.00E+030

 

10

 

0

 

5

 

5 1.00E+030

 

5

 

2

 

5

 

1

 

1

 


 

From

 

1

 

1

 

1

 

1

 

2

 

2

 

2

 

2

 

Total Cost

 


 

To

 

3

 

4

 

5

 

6

 

3

 

4

 

5

 

6

 


 

Cost

 

54

 

17

 

23

 

30

 

24

 

18

 

19

 

31

 


 

Flow

 

0

 

10

 

1

 

5

 

9

 

0

 

9

 

0

 


 

730

 


 

Questions to Answer

 

a. In the optimal solution, is the constraint on meeting the minimum demand for location 4 binding? (2 points)

 


 

b. The current cost of transporting a car from location 1 to location 5 is $23. Over what range of that cost does the current tra

 

Lower End of Range

 

Upper End of Range

 


 

c. In the optimal solution, the company should not move any cars from location 2 to location 4. How much would the per unit t

 

from location 2 to location 4? (If the per unit transport cost needs to increase, enter a positive number. If it needs to decrease

 


 

d. If the supply of cars at location 2 increased to 19, what would be the resulting total cost? (If you can?t say for sure what the

 

In this worksheet, explain as much as possible about the change in the total cost.) (4 points)

 


 

e. If the maximum demand for cars at location 5 were to decrease to 9, what would be the resulting total cost? (If you can?t sa

 

In this sheet, explain as much as possible about the change in the total cost.) (4 points)

 


 

Node

 

1

 

2

 


 

Flow Out

 

16

 

18

 


 

Supply

 

16

 

18

 


 

Node

 

3

 

4

 

5

 

6

 


 

Flow In

 

9

 

10

 

10

 

5

 


 

Min. Demand

 

5

 

5

 

5

 

5

 


 

Max Demand

 

10

 

10

 

10

 

10

 


 

n 4 binding? (2 points)

 


 

t range of that cost does the current transporting plan remain optimal? (4 points)

 


 

cation 4. How much would the per unit transport cost have to change before it would become optimal to move at least one car

 

positive number. If it needs to decrease, enter a negative number.) (4 points)

 


 

ost? (If you can?t say for sure what the total cost will do, enter ?Can?t say? in the summary sheet.

 


 

the resulting total cost? (If you can?t say for sure what the total cost will do, enter ?Can?t say? in the summary sheet.

 


 

at least one car

 


 

 

Paper#9210367 | Written in 27-Jul-2016

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