Explanation Given: The cost equation is given as C ( x ) = 90 , 000 + 30 x where x is the paper shredders. Procedure used: 1. Select the variables and find the some relations among the variables. 2. Form a mathematical model as shown below. Maximize ( or minimize ) f ( x ) on the interval I 3. Obtain the critical numbers of f ( x ) . 4. Use second derivative test to check for absolute maximum (or minimum) and find the absolute maximum (or minimum) of f ( x ) on the interval I and the numbers x as the absolute maximum must occur either at the critical points or at the endpoints with the help of substitution. 5. Find the values of the left variables with the help of the solution obtained in step 4. Calculation: From matched problem 3, use the revenue equation in order to find the profit equation. Obtain the profit function where R ( x ) = 300 x − x 2 30 and C ( x ) = 90 , 000 + 30 x as follows. Profit = Revenue − C ost P ( x ) = R ( x ) − C ( x ) P ( x ) = 300 x − x 2 30 − ( 90 , 000 + 30 x ) P ( x ) = − x 2 30 + 270 x − 90 , 000 . In order to find the maximum profit, the problem that should be computed becomes, Maximize P ( x ) = − x 2 30 + 270 x − 90 , 000 subject to 0 ≤ x ≤ 9 , 000 . Set P ′ ( x ) = 0 and find the critical numbers of P as follows

Pearson eText for College Mathematics for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)

14th Edition

ISBN: 9780137553341

Author: Raymond Barnett, Michael Ziegler

Publisher: PEARSON+

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Chapter 11.6, Problem 4MP

To determine

To find: The maximum profit, the price charged by company for the shredders that leads to maximum profit and the number of shredders.

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Chapter 11.6, Problem 3MP

Chapter 11.6, Problem 5MP

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Chapter 11 Solutions

Pearson eText for College Mathematics for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)

Ch. 11.1 - Matched Problem 1 Repeat Example 1 for f(x) = x2 –...Ch. 11.1 - Matches Problem 2 Find the critical numbers of f,...Ch. 11.1 - Matched Problem 3 Find the critical numbers of f,...Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 7MP Ch. 11.1 - Prob. 8MP Ch. 11.1 - Prob. 9MP Ch. 11.1 - Skills Warm-up Exercises In Problems 1-8, inspect...

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