The L. Young & Sons Manufacturing Company produces two products, which have the following profit and resource requirement characteristics:

Last month’s production schedule used 350 hours of labor in department A and 1000 hours of labor in department B. Young’s management has been experiencing workforce morale and labor union problems during the past six months because of monthly departmental workload fluctuations. New hiring, layoffs, and interdepartmental transfers have been common because the firm has not attempted to stabilize workload requirements. Management would like to develop a production schedule for the coming month that will achieve the following goals:
Goal 1: Use 350 hours of labor in department A.
Goal 2: Use 1000 hours of labor in department B.
Goal 3: Earn a profit of at least $1300.
a. Formulate a goal programming model for this problem, assuming that goals 1 and 2 are P1 level goals and goal 3 is a P2 level goal; assume that goals 1 and 2 are equally important.
b. Solve the model formulated in part (a) using the graphical goal programming procedure.
c. Suppose that the firm ignores the workload fluctuations and considers the 350 hours in department A and the 1000 hours in department B as the maximum available. Formulate and solve a linear programming problem to maximize profit subject to these constraints.
d. Compare the solutions obtained in parts (b) and (c). Discuss which approach you favor, and why.
e. Reconsider part (a) assuming that the priority level 1 goal is goal 3 and the priority level 2 goals are goals 1 and 2; as before, assume that goals 1 and 2 are equally important. Solve this revised problem using the graphical goal programming procedure, and compare your solution to the one obtained for the original problem.

Transcribed Image Text:

Product 1 $4 Characteristic Profit/unit Dept. A hours/unit Dept. B hours/unit Product 2 $2