The Elastic Firm has two products coming on the market, Zigs and Zags. To make a Zig, the firm needs 10 units of product A and 15 units of product B. To make a Zag, they need 20 units of product A and 15 units of product B
There are only 2,000 units of product A and 3,000 units of product B available to the firm. The profit on a Zig is $4 and on a Zag it is $6. Management objectives in order of their priority are:
1. Produce at least 40 Zags.
2. Achieve a target profit of at least $750.
3 . Use all of the product A available.
4. Use all of the product B available.
5. Avoid the requirement for more product A.
Formulate this as a goal programming problem.
Let X1 = number of Zigs, X2 = number of Zags.
d1- = underachievement of Zag goal
d1+ = overachievement of Zag goal
d2- = underachievement of profit target
d2+ = overachievement of profit target
d3- = unused product A
d3+ = additional amount of product A needed
d4- = unused product B
d4+ = additional amount of product B needed
Minimize P1 d1- + P2 d2- + P3 d3- + P4 d4+ + P5 d3-
Subject to: X2 + d1- - d1+ = 40 (Zag constraint)
4 X1 + 6 X2 + d2- - d2+ = 750 (profit)
10 X1 + 20 X2 + d3- - d3+ = 2000 (product A)
15 X1 + 15 X2 + d4- - d4+ = 3000 (product B)
all variables ? 0
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