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 the firm needs 20 units of product A and 15 units of product B. There are only 2000 units of product A and 3000 units of product B available to the firm. The profit on a Zig is $4 and on a Zag is $6. Management objectives in order of their priority are:

(1) Produce at least 50 Zigs.

(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.

(a) Formulate this as a goal programming problem.

(b) What modification(s) to your goal program formulated in (a) is/are necessary if the fourth goal is removed from the above objective list?

(c) What modification(s) to your goal program formulated in (a) are necessary if a fifth goal (fifth priority) is added stating that "If the first goal is not achieved, the amount of underachievement should not exceed 5 Zigs"?