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:

One Hundredth

A fractional unit that is one part of a hundred, commonly expressed as 1/100.

Hydro-

A prefix indicating relation to water.

Hydrotherapy

The use of water in the treatment of different conditions, including arthritis and related rheumatic complaints.

Water

A colorless, odorless, tasteless liquid that forms the seas, lakes, rivers, and rain, and is the basis of the fluids of living organisms.