Question: The Metro Food Services Company delivers fresh sandwiches each morning to vending machines throughout the city. The company makes three kinds of sandwiches- ham and cheese, bologna, and chicken salad. A ham and cheese sandwich requires a worker 0.45 minutes to assemble, a bologna sandwich requires 0.41 minutes, and a chicken salad sandwich requires 0.50 minutes to make. The company has 960 available minutes (16 hours) each night for sandwich assembly. Vending machine capacity is available for 2000 sandwiches each day. The profit for a ham and cheese sandwich is $0.35, the profit for a bologna sandwich is $0.42, and the profit for a chicken salad sandwich is $0.37. The company knows from past sales records that their customers buy as many or more of the ham and cheese sandwiches than the other two sandwiches combined, but customers need a variety of sandwiches available, so Metro stocks at least 200 of each. Metro Management wants to know how many of each sandwich it should stock to maximize profit.


a. Formulate a linear programming model for this problem. Clearly state your decision variables, objective function, and the constraints.

b. Solve the linear programming problem you formulated in part (b) using the computer (EXCEL or QM WINDOWS).

c. If Metro Food Services could hire another worker and increase its available assembly time by 8 hours (480 minutes), or increase its vending machine capacity by 100 sandwiches, which should it do? Why? How much additional profit would your decision result in?

d. What would the effect be on the optimal solution if the requirement that at least 200 sandwiches of each kind be stocked were eliminated? Compare the profit between the optimal solution and this solution, and indicate which solution you would recommend.

e. What would the effect be on the optimal solution if the profit for a ham and cheese sandwich were increased to $0.40?

f. What would the effect be on the optimal solution if the profit for a ham and cheese sandwich were increased to $0.45?