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. 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.

Question

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. 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.

Quizplus · Accepted Answer

The Answer of 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. 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.