A company has three manufacturing plants (in Atlanta, Tulsa, and Springfield) that produce a product that is then shipped to one of four distribution centers. The three plants can produce 13, 18, and 12 truckloads of product each week, respectively. Each distribution center needs 10 truckloads of product each week. The shipping costs per truckload between the plants and distribution centers are given in the table. The company needs to determine how much to ship from each plant to each distribution center and would like to minimize total shipping costs.

                                

(a) Formulate an LP to minimize the total shipping costs.
(b) Set up and solve the problem on a spreadsheet.
(c) What is the optimal solution? Explain the rationale for the solution.