20% 2, Consider the following linear programming problem Max Profit:500A+700B Su

Question

20% 2, Consider the following linear programming problem Max Profit:500A+700B Subject to: A +3Bs35 (assembly hours) A+SB s40 (machine hours) A, B20 Reformulate this problem as a goal programming problem if the following goals, with their associated weights, are to 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

Explanation / Answer

Let djp and djn be the positive and negative deviation variable respectively for goal j , where j ={1,2,3,4,5} for the five goals

Objective : Min 15d1n + 15d2n + 25d3p + 25d4p + 20d5n

A-d1p+d1n = 15

B-d2p+d2n = 15

A+3B-d3p+d3n = 35

3A+5B-d4p+d4n = 40

500A+700B-d5p+d5n = 100000

All variables >= 0

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