Management problem. Analytic solver may be needed beyond the regular excel solver.

1. A company has three products (P1, P2, and P3) that are produced with three main resources (R1, R2, and R3. A manger in the company formulated a profit-maximization linear programming model to find an optimal solution to the product-mix problem involving these products and resources. This is the Sensitivity Report associated with the optimal solution of the linear programming model that the manager formulated. Adjustable Cells Final Allowable Allowable Name Value Increase Decrease P1 1E+30 Reduced Objective Cost Coefficient 0 2100 -500 900 0 1050 Cell $C$10 $C$11 $C$12 350 9.52 0.00 9.13 P2 500 1E+30 375 P3 210 Constraints Final Value Shadow Price Constraint R.H. Side Allowable Increase Allowable Decrease Name R1 18.65 0 20 1E+30 1.35 R2 28.17 0 50 1E+30 21.83 Cell $C$13 $D$13 $E$13 $F$10 $F$11 $F$12 R3 7500.00 3.50 7500 404.76 2738.10 P1 0.02 200000 115000 42500.00 200000.00 0.00 P2 0 180000 1E+30 180000.00 48055.56 P3 31944.44 0 80000 1E+30 Use the Sensitivity Report to answer the following questions. a. Suppose the company can purchase more R3 for $2.50 per unit, should the company purchase it and how much can the company buy and still be sure of the value of the additional units of R3? b. Suppose that the profit of P1 drops to $1,800 per unit. Is it still profitable to produce P1? C. Suppose that the profit of P3 increases to $1,200 per unit. Should the company produce more than 9.13 units of P3? d. What must the minimum profit per unit of P2 be in order to make it worthwhile to produce? The company is considering a new type of product that requires 1.5 units of R2 and 200 units of R3. What must the minimum profit per unit of the new product be in order to make it worthwhile to produce? e