HW 3 SOLUTION|ALL YOU NEED

HW 3 SOLUTION 1. An appliance manufacturer produces two models of microwave ovens: model H and model W. Both models require fabrication and assembly work; each H uses four hours of fabrication and two hours of assembly, and each W uses two hours of fabrication and six hours of assembly. There are 600 fabrication hours available this week and 480 hours of assembly. Each H contributes $40 to profits and each W contributes $30 to profits. a. Formulate this problem as a linear program. b. Use the graphical solution method (e.g., corner-point method) to determine the quantities of H and W that will maximize total profit. Solution: a. Maximize Z = $40H + $30W subject to: Fabrication: 4H + 2W  600 hours Assembly 2H + 6W  480 hours Non-negativity: H, W ≥ 0 b. Corner-Point Method: (H, W)  (0, 80) : Z = $2,400  (150, 0) : Z = $6,000  (132, 36) : Z = $6,360 (optimum)  (0, 0) : Z = $0 Optimum solution: H = 132 units and W= 36 units with objective function value of Z = $6,360. 300 250 200 150 100 50 0 Assembly W H Fabrication  80 optimum 240 This study re