Question 2

Question 2 The following linear program model is used to optimize the production of four products (X1, X2,X3 and X4 ), with two different manufacturing processes and two different material requirements. Maxs.t.Z=$48X1+$52X2+$57X3+$60X44X1+2.1X2+2.6X3+3.9X45003.5X1+4.6X2+3.5X3+1.9X460015X1+21X2+19X3+22X435007.5X1+11.5X2+9.5X3+10.6X41600X1,X2,X3,X40(Totalprofit)(Process1)(Process2)(MaterialA)(MaterialB) The linear program model is solved using Excel Solver and sensitivity reports are given as below: Adictahle r.alle Based on the sensitivity reports, answer the following questions: (a) What is the optimal production mix and total profit? (5 marks) (b) Holding all other factors remain unchanged, what is the profit contribution of Product 1 so that the optimal production mix remains the same. (2 marks) (c) Which is the most valuable resource to the firm? Why? (2 marks) (d) One of the four products is not produced in the optimal mix. What would the profit become if one unit of such a product was produced while other conditions remain the same? (2 marks) (e) If the manufacturer can obtain an extra amount of 100 units of Material B at the price of $4.0 each, should he do so or not? Explain. What is the new total profit? (4 marks)