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. Max Z = $48X1 + $52X2 + $57X3 + $60X4 (Total profit) s.t. 4X1 + 2.1X2 + 2.6X3 + 3.9X4 500 (Process 1) 3.5X1 + 4.6X2 + 3.5X3 + 1.9X4 600 (Process 2) 15X1 + 21X2 + 19X3 + 22X4 3500 (Material A) 7.5X1 + 11.5X2 + 9.5X3 + 10.6X4 1600 (Material B) X1 , X2 , X3 , X4 0 The linear program model is solved using Excel Solver and sensitivity reports are given as below: Adjustable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$15 Product 1 29.10 0 48 25.35 1.68 $C$15 Product 2 0 -17.02 52 17.02 1E+30 $D$15 Product 3 139.37 0 57 1.40 7.23 $E$15 Product 4 5.44 0 60 5.14 4.56 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $F$18 Process 1 500 0.72 500 268.93 34.29 $F$19 Process 2 600 2.16 600 12.97 135.19 $F$20 Material A 3204.35 0 3500 1E+30 295.65 $F$21 Material B 1600 5.01 1600 141.53 48.98 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)