426 CHAPTER9 Derivatives In business and economics, common questions of interest

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426 CHAPTER9 Derivatives In business and economics, common questions of interest include or revenue, how to minimize average costs, and how to tions of interest include how to maximize peofix w to maximize minimum represents an optimal (or best possible) solution to th cess of finding an optimal solution is called optimization, olem, ofiten involves tangent lines. In this project, we examine how tan minimize average costs. For questions such as these, the description of how to obtain the dverage Answering angent t lines can be used to Suppose that Wittage, Inc, manufactures paper shredders for h and that its weekly total costs (in dollars) for x shredders home and office u are given by ar) = 0.03x2 + 12.75x + 6075 l cost divided by the nun- ber of units. Thus, the average cost function for Wittage, Inc., is 6075 as)-ax) = 0.03x, + 12.75x + 6075= 0.03x2 + 12.75x ax) = 0.03x + 12.75 + Wittage, Inc., would like to know how the company can use marginal costs to gain infor. mation about minimizing average costs. To investigate this relationship, answer the questions. 1. Find Wittage's marginal cost function, then complete the following table. 100 200 300 400 500 600 2. (a) For what -values in the table is C getting smaller? (b) For these x values, is MC C, or MC- 3. (a) For what x-values in the table is C getting larger? (b) For these x-values, is- C, or MC- 4. Between what pair of consecutive x-values in the table w 5. Interpret (a) C (200) and MC(200) and (b) C(400) and MC(400). 6. On the basis of what C and MC tell us and the work so far, complete the hinrur reach its minimum statements by filling the blank with increase, decrease, or stay the sa reasoning (a) MC ? means that if Wittage makes one more unit,then C will (a) ?will- 7. On the basis of your answersto Question 6, how will?and MC be C is minimized? Write a careful statement. related who related wher (b) Use your idea from calculations by graphing and locating the minimum from the g part (a) to find x where C is minimized. Then

Explanation / Answer

Ans 9)

a)

Slope of segment AB is less than Slope of segment CD hence change in cost with respect to change in quantity for AB is less than that of CD

b)

For Simlar reason mentioned above  change in cost with respect to change in quantity for QR is less than that of ST

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