Table 10-7
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 30 units of product B.There are only 2,000 units of product A and 3,200 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 exactly 50 Zigs.
(2) Achieve a target profit of at least $750.
(3) Use all of the product B available.
Let X₁ = number of Zigs,X₂ = number of Zags.
d₁^- = underachievement of Zig goal
d₁⁺ = overachievement of Zig goal
d₂^- = underachievement of profit target
d₂⁺ = overachievement of profit target
d₃^- = unused product B
d₃⁺ = additional amount of product B needed
-In the goal programming problem described in Table 10-7,how is the goal of achieving a target profit of at least $750 expressed?

Question

Quizplus · Accepted Answer

The expression for achieving a target profit of at least $750 is given as: 4X₁ + 6X₂ + d₂^- - d₂⁺ = 750 This expression includes the profit from both Zigs and Zags (4*X₁ and 6*X₂), as well as the underachievement and overachievement variables for the profit target. The goal is to find values for X₁ and X₂ that satisfy this expression while also satisfying the other management objectives.

Table 10-7 The Elastic Firm Has Two Products Coming on the Market