***I need help on problems 6-10. Answers for 1-4 are above, and answer to number
ID: 2892841 • Letter: #
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***I need help on problems 6-10. Answers for 1-4 are above, and answer to number 5 is C(200) = 49.125 and M(400)= 24.75
ended Applications Ill. Tangent Lines and Optimization in Business and Economics In business and economics, common questions of interest include how t maximiz profit or revenue, how to minimize average costs, and how to maximize average pro- ductivity. For questions such as these, the description of how to obtain the desired max. imum or minimum represents an optimal (or best possible) solution to the problem. And the process of finding an optimal solution is called optimization. Often answering these questions involves tangent lines. In this project, we examine how tangent lines can be used to minimize average costs Suppose that Wittage, Inc. manufactures paper shredders for home and personal use and that its weekly total costs (in dollars) for x shredders are given by 0.03 12.75x 6075 The average cost per unit for x units (denoted by CCx)) is the total cost divided by the number of units. Thus, the average cost function for Wittage, Inc. is C(x) 0.03x2 12.75x 6075 0.032 12.75x 6075 C(x) 6075 C 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 fol- lowing questions. l. Find Wittage's marginal cost function, then complete the following table. 100 200 300 400 500 600 C(r) 2. (a) For what x-values in the table is C getting smaller? (b) For these x-values, is MC C, MC C, or MC 3. (a) For what x-values in the table is C getting larger? (b) For these x-values, is MC C, MC C, or MC 4. Between what pair of consecutive x-values in the table will C reach its minimum? 5. Interpret (a) CO200) and MC200) and (b) CO400) and MC(400) 6. On the basis of what Cand MC tell us, and the work so far, complete the follow- ing statements by filling the blank with increase, decrease or stay the same. Explain your reasoning (a) MC C means that if Wittage makes one more unit, then C will (b) MC C means that if Wittage makes one more unit, then C will 7. (a) on the basis of your answer to question 6, how will Cand MC be related when C is minimized? Write a careful statement. (b) Use your idea from part (a) to find x where C is minimized. Then check your calculations by graphing Cand locating the minimum from the graph.Explanation / Answer
Question 6:
(a) If MC<C, then cost will decrease.
(b) If MC>C, then cost will increase.
Question 7:
(a) When cost C is minimum, MC = C.
(b) On setting MC=C, and solving for x (or looking at the intersection of two graph) we get, x = 450
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