Question

ASuppose you have 3 plants where you can produce windows and doors. Each window must be processed at Plant 1 and Plant 3. Each door must be processed at Plant 2 and Plant 3. Available working hours and profits of each final product (window and door) are given below: Plant Window (hr/unit) Door (hr/unit) Available Working Hours 1 1 0 4 2 0 2 12 3 3 2 18 Profit 3 $/ unit 5 $/ unit For example, the table above indicates that one window can be produced in Plant 1 in one hour and has a profit of 3$, where Plant 1 has available 4 hours for production. The aim is to maximize total profit while producing products within available working hours. (a) Formulate the LP model and solve it using Graphical Method. (b) Suppose that available working hours of Plant 2 is changed from 12 to 14. Does the optimal solution change? (c) Find the maximum value for the available working hours of Plant 2, so that the new constraint remains binding? (d) What happens to the optimal solution if profit of one unit window (3$) is replaced with 4$? (e) How large can the profit of one unit window be, for your answer to stay correct?

Answer 1

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