Question

In: Advanced Math

Three materials X, Y, and Z are required to produce two products A and B. The...

Three materials X, Y, and Z are required to produce two products A and B. The profit function of each product is nonlinear. The total profit function for Product A is 80A - A2 and the total profit function for Product B is 72B - 0.8B2. Thus, the total profit 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) to solve the nonlinear profit function for this problem. (Note: this problem does not have a constraint.) What is the optimal production quantity for each product? What is the total profit? Why is the solution optimal? Is the total profit function a function with decreasing marginal return? Why?

b. Following information about resource requirement and availability is given. Formulate the problem with constraints as a nonlinear programming model on the spreadsheet to maximize 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 Nonlinear Solver. What is the optimal solution? What is the maximum total profit?

D. Explain why solutions in (a) and (c) are different.

E. Formulate the problem in (b) as an algebraic model.

Expert Solution

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a)

The model is shown below

The formulas are shown below

The solver parameters are shown below

The result is shown below. The optimal values are A = 40 and B = 45 and the profit is 3220.

b)

The model is shown below

The formulas are shown below

The solver parameters are shown below

c)

The result is shown below. The optimal values are A = 24.33, B = 20.52 and the profit is 2495.66

d)

The reason why the results are different is because of the constraints in the part c).

PLEASE LIKE AND RATE GOOD .. IT IS VERY LEANTHY QUESTION.

Colby Messinger answered 2 years ago

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