A manufacturing company produces products 1, 2, and 3. The three products have the following resource requirements and produce the following profit:

Product Labor (hr./unit) Material (lb./unit) Profit ($/unit)

1 5 4 $3 2 2 6 5 3 4 3 2 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:

maximize Z = 3x1 + 5x2 + 2x3 subject to 5x1 + 2x2 + 4x3 … 240 4x1 + 6x2 + 3x3 … 400 x1, x2, x3 Ú 0 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. LO.1