4. Formulate only. Define all your variables first. Theze aze decision variables

Question

4. Formulate only. Define all your variables first. Theze aze decision variables in this problem. Ace Manufacturing produces two products A and B according to the following data chart. Product A Product B Material (parts per unit product) Labor (hrs. per unit product) Equipment (hrs. per unit product) Profit per unit product 530 $25 The general manager has prioritized the following goals. PI. Manufacture at least 7 units of product à and 10 units of product B. P2. Avoid using more than 95 parts of material, 130 worker hours, and 110 equipment hours P3. Achieve a target profit of $850 exactly

Explanation / Answer

There are __ 14 __ decision variables. 2 of them are standard variables, and 12 are deviation variables.

Standar variables:

A = Number of product A to produce

B = Number of product B to produce

Objective: Min 3d1- + 3d2- + 2d3+ + 2d4+ + 2d5+ + d6+ d6-

Constraints:

A - d1+ + d1- = 7

B - d2+ + d2- = 10

7A + 4B - d3+ + d3- = 95

2A + 5B - d4+ + d4- = 130

6A + 9B - d5+ + d5- = 110

30A + 25B - d6+ + d6- = 850

A, B, d1+, d1-, d2+, d2-, d3+, d3-, d4+, d4-, d5+, d5-, d6+, d6- >= 0

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