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Suppose the cost function in dollars for a certain amount, x, of a product is given by C(x)=120x-3x² +0.1x³ and the revenue function in dollars for a certain amount, x, is given by R(x)=30x² -0.9x³. Determine the following: 1. The profit function P(x)=_ 2. The marginal profit function. 3. The critical values of x..

Suppose the cost function in dollars for a certain amount, x, of a product is given by C(x)=120x-3x² +0.1x³ and the revenue function in dollars for a certain amount, x, is given by R(x)=30x² -0.9x³. Determine the following: 1. The profit function P(x)=_ 2. The marginal profit function. 3. The critical values of x..

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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ECONOMICS AND CALCULUS A DERIVATIVE APPROACH Suppose the cost function in dollars for a certain amount, x, of a product is given by C(x)=120x-3x² +0.1x³ and the revenue function in dollars for a certain amount, x, is given by R(x)=30x² -0.9x³. Determine the following: 1. The profit function P(x)=_ 2. The marginal profit function. 3. The critical values of x.. 4. The interval/s of x where profit is increasing.. 5. The marginal profit at x=15 units of product. 6. The value of x that yields maximum profit._ 7. The optimal profit in dollars._ 8. The value/s of x, if any, at which inflection/s occur. 9. The interval/s, if any, where profit is increasing yet slowing down._ 10. The rate of change of marginal profit at x=25._
Transcribed Image Text:ECONOMICS AND CALCULUS A DERIVATIVE APPROACH Suppose the cost function in dollars for a certain amount, x, of a product is given by C(x)=120x-3x² +0.1x³ and the revenue function in dollars for a certain amount, x, is given by R(x)=30x² -0.9x³. Determine the following: 1. The profit function P(x)=_ 2. The marginal profit function. 3. The critical values of x.. 4. The interval/s of x where profit is increasing.. 5. The marginal profit at x=15 units of product. 6. The value of x that yields maximum profit._ 7. The optimal profit in dollars._ 8. The value/s of x, if any, at which inflection/s occur. 9. The interval/s, if any, where profit is increasing yet slowing down._ 10. The rate of change of marginal profit at x=25._
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