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P09 - Project 9 MAC 2311 In this project we explore the...

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Project 9 MAC 2311 In this project, we explore the average and instantaneous rates of change of total cost, total rev- enue, and total profit with respect to the number x of items produced/sold. In particular, note the interpretations of the calculations, and how they might impact important decisions. 1. Suppose the total cost C ( x ) of producing x books is C ( x ) = 1200 + x 2 - 20 x , represented by \$1200 in storage costs, x 2 dollars for materials and labor, and a \$20 rebate from the govern- ment for each book produced. What is the total cost of producing 0 books? 20 books? What is the average change in cost per book of producing the first twenty books? What is the average change in total cost as x changes from 25 to 30 . What does this imply about the extra cost incurred by producing each of books number 26 through 30 ? What is the total cost of producing 35 books? 36 books? What, then, is the extra cost incurred from producing the 36 th book? Calculate the instantaneous rate of change in total cost when x = 35 . (Indicate the units for your answer.) How close is this to the cost you calculated above?

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P09 - Project 9 MAC 2311 In this project we explore the...

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