Data Equipment Inc produces two models of a retail price scanner, a sophisticated model that can be networked to a central processing unit and a stand-alone model for small retailers

Question

The major limitations of the manufacturing of these two products are labor and material capacities. The following table summarizes the usages and capacities associated with each product.

The typical LP formulation for this problem is:

Maximize $160 X1 + $95 X2
Subject to: 8 X1 + 5 X2 ? 800
20 X1 + 7 X2 ? 1500
X1, X2 ? 0

However, the management of DEI has prioritized several goals that are to be attained by manufacturing:
1. Since the labor situation at the plant is uneasy (i.e., there are rumors that a local union is considering an organizing campaign), management wants to assure full employment of all its employees.
2. Management has established a profit goal of $12,000 per day.
3 . Due to the high prices of components from nonroutine suppliers, management wants to minimize the purchase of additional materials.

Given the above additional information, set this up as a goal programming problem.

Answer 1

Let d1- = underachievement of full employment goal
d1+ = overachievement of full employment goal
d2- = underachievement of profit target
d2+ = overachievement of profit target
d3- = unused components
d3+ = additional amount of components needed

Minimize P1 d1- + P2 d2- + P3 d3+
Subject to: 8 X1 + 5 X2 + d1- - d1+ = 800
160 X1 + 95 X2 + d2- - d2+ = 12000
20 X1 + 7 X2 + d3- - d3+ = 1500
all variables ? 0