An appliance manufacturer produces two models of microwaves: H and 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 6 hours of assembly. There are 600 fabrication hours available this week and 480 hours of assembly. Each H contributes $40 to profit and each W contributes $30 to profit. Develop a linear programming model to maximize the total profit for this company.
(a) Solve this LP model graphically to evaluate the quantities of H and W that maximize the profit?
(b) What will be the maximum profit?
(c) If the profit per unit of H increased by $5, will the optimal solution be changed? If yes, what will be the new optimal solution?
(d) If the profit per unit of W decreased by $5, will the optimal solution be changed? If yes, what will be the new optimal solution?