Consider the Following Linear Programming Problem Reformulate and Solve This Problem as a Goal Programming Problem

question 41

Essay

Consider the following linear programming problem:
$$\begin{array} { l } \text { Max: } 500 A + 700 B \\\text { Subject to: } \\2 A + 3 B \leq 35 \text { (assembly hours) } \\3 A + 5 B \leq 40 \text { (machine hours) }\end{array}$$
Reformulate and solve this problem as a goal programming problem if the following goals,with their associated weights,must be met.
Goal 1: Produce at least 15 units of product A;Weight 15
Goal 2: Produce at least 15 units of product B;Weight 15
Goal 3: Minimize overtime in assembly department;Weight 25
Goal 4: Minimize overtime in machine department;Weight 25
Goal 5: Achieve at least $100,000 in profit;Weight 20

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Definitions:

Materials Price Variance

The variance between the standard cost and the actual expense of materials, calculated by multiplying the amount bought.

Direct Materials

Raw materials that are directly traceable to the production of a specific product, representing a significant portion of the costs of goods sold.

Variable Overhead Rate Variance

The difference between the actual variable overhead costs incurred and the expected costs based on the predetermined overhead rate.

Direct Materials

Raw materials that are directly traceable and allocable to the production of specific goods or services.