Suppose a ceiling fan manufacturer has the total cost function C(x) = 35x + 1200 and the total revenue function R(x) = 65x. (a) What is the equation of the profit function P(x) for this commodity? P(x) = (b) What is the profit on 20 units? P(20) = Interpret your result. The total costs are less than the revenue. The total costs are more than the revenue. The total costs are exactly the same as the revenue. (c) How many fans must be sold to avoid losing money? fans

Suppose a ceiling fan manufacturer has the total cost function C(x) = 35x + 1200 and the total revenue function R(x) = 65x. (a) What is the equation of the profit function P(x) for this commodity? P(x) = (b) What is the profit on 20 units? P(20) = Interpret your result. The total costs are less than the revenue. The total costs are more than the revenue. The total costs are exactly the same as the revenue. (c) How many fans must be sold to avoid losing money? fans

Essentials of Business Analytics (MindTap Course List)

2nd Edition

ISBN:9781305627734

Author:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Publisher:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Chapter13: Nonlinear Optimization Models

Section: Chapter Questions

Problem 2P: The Cobb-Douglas production function is a classic model from economics used to model output as a...

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The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form: f(L,C)=c0Lc1Cc2, where c0, c1, and c2 are constants. The variable L represents the units of input of labor, and the variable C represents the units of input of capital. a. In this example, assume c0 = 5, c1 = 0.25, and c2 = 0.75. Assume each unit of labor costs 25 and each unit of capital costs 75. With 75,000 available in the budget, develop an optimization model to determine how the budgeted amount should be allocated between capital and labor in order to maximize output. b. Find the optimal solution to the model you formulated in part (a). (Hint: When using Excel Solver, use the Multistart option with bounds 0 L 3,000 and 0 C 1,000.)
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