Chapter 4, Problem 19QP

Use Solver to create a Sensitivity Report for question 23 at the end of chapter 3 and answer the following questions:

1. a. Is the optimal solution unique? How can you tell?
2. b. Which location is receiving the fewest cars?
3. c. Suppose a particular car at location 1 must be sent to location 3 in order to meet a customer’s request. How much does this increase costs for the company?
4. d. Suppose location 6 must have at least eight cars shipped to it. What impact does this have on the optimal objective function value?

23. The Rent-A-Dent car rental company allows its customers to pick up a rental car at one location and return it to any of its 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 summarized in the following table.

Because 34 surplus cars are available at locations 1 and 2, and 40 cars are needed at locations 3, 4, 5, and 6, 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 that each location needing cars receives at least five.

1. a. Formulate an LP model for this problem.
2. b. Create a spreadsheet model for this problem and solve it using Solver.
3. c. What is the optimal solution?