# solvertable using mathematical optimization problems for shipping hw4 1

1. (Chapter 5 in Edition 4 – Question 67: Allied Freight)

Allied Freight supplies goods to three customers, who each require 30 units. The company has two warehouses. In warehouse 1, 40 units are available, and shipping one unit from each warehouse to each customer are shown in the file P05-67.xlsx. There is a penalty for each unsatisfied customer unit of demand: with customer 1, a penalty cost of \$90 is incurred; with customer 2, \$80; and with customer 3, \$110.

a. Determine how to minimize the sum of penalty and shipping costs.

b. Use SolverTable to see how a change in the unit penalty cost of customer 3 affects the optimal cost.

c. Use SolverTable to see how a change in the capacity of warehouse 2 affects the optimal cost.

2. Solve the following modifications of the capital budgeting model in Figure 6.4. (Solve each part independently of the others.) For each case first write the mathematical optimization problem. Then use Excel Solver to solve and find an optimal solution.

a. Suppose that at most two of projects 1 through 5 can be selected.

b. Suppose that if investment 1 is selected, then investment 3 must also be selected.

c. Suppose that at least one of investments 6 and 7 must be selected.

d. Suppose that investment 2 can be selected only if both investments 1 and 3 are selected.

3. (Chapter 6 in Edition 4- Question 11: Great Threads)

How difficult is it to expand the Great Threads model to accommodate another type of clothing? Answer by assuming that the company can also produce sweatshirts. The rental cost for sweatshirt equipment is \$1100; the variable cost per unit and the selling price are \$15 and \$45, respectively; and each sweatshirt requires one labor hour and 3.5 square yards of cloth.

4. (Chapter 6 in Edition 4- Question 28: Set Covering)

In the United Copiers service center model, we assumed that the potential locations of service centers are the same as existing customer locations. Change the model so that the customer locations are the ones given, but the only potential service center locations are in Memphis, Houston, Cleveland, Buffalo, Minneapolis, St. Louis, and Kansas City. You can look up the distances from these cities to the customer cities in a reference book or on theWeb, or you can make up approximate distances. Use Solver to find the optimal solution.