Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 36

A manufacturing company produces products 1, 2, and 3. The three products have the following resource requirements and produce the following profit:
At present, the firm has a daily labor capacity of 240 available hours and a daily supply of 400 pounds of material. The general linear programming formulation for this problem is as follows:

Management has developed the following set of goals, arranged in order of their importance to the firm:
(1) Because of recent labor relations difficulties, management wants to avoid underutilization of normal production capacity.
(2) Management has established a satisfactory profit level of $500 per day.
(3) Overtime is to be minimized as much as possible.
(4) Management wants to minimize the purchase of additional materials to avoid handling and storage problems.
Formulate a goal programming model to determine the number of each product to produce to best satisfy the goals.