- Three materials X, Y, and Z are required to produce twoproducts A and B. The profit function of each product is nonlinear.The total profit function for Product A is 80A - A2 and the totalprofit function for Product B is 72B - 0.8B2. Thus, the totalprofit for producing A and B together is 80A - A2
+ 72B - 0.8B2. (These two profit functions are independent.)
a. Use the Nonlinear Solver (GRG Nonlinear) tosolve the nonlinear profit function for this problem. (Note: thisproblem does not have a constraint.) What is the optimal productionquantity for each product? What is the total profit? Why is thesolution optimal? Is the total profit function a function withdecreasing marginal return? Why?
b. Following information about resourcerequirement and availability is given. Formulate the problem withconstraints as a nonlinear programming model on the spreadsheet tomaximize the total profit.
| Product A | Product B | Materials Available (kilograms) |
Material X | 0.8 | 1.0 | 40 |
Material Y | | 0.4 | 10 |
Material Z | 1.2 | 0.6 | 42 |
Profit Function | 80A - A2 | 72B - 0.8B2 | |
C. Solve the problem using the NonlinearSolver. What is the optimal solution? What is the maximum totalprofit?
D. Explain why solutions in (a) and (c) aredifferent.
E. Formulate the problem in (b) as an algebraicmodel.
