Suppose that the total cost (in dollars) for a product is given byC(x)=1300+ 160 In(2x + 1)where x is the number of units produced.(a) Find the marginal cost MC function.MC =(b) Find the marginal cost when 160 units are produced. (Round your answer to the nearest cent.)$Interpret your result.The profit from the next unit will be approximately this amount.This is the total cost of producing 160 units.◇ This is the total profit from producing 160 units.○ It will cost approximately this amount to make the next unit.(c) Total cost functions always increase because producing more items costs more. What then must be true ofthe marginal cost function?○ MC ≥ 0○ MC > 0○ MC ≤ 0○ MC = 0○ MC <0Does it apply in this problem?○ YesΟ ΝΟ

Given:Total cost: C (x) = 1,300 + 160ln(2x + 1) (a) MC = 320 / (2x + 1)Derive the MC from the total…

Answered: Suppose that the total cost (in…

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter4: Extent (how Much) Decisions

Section: Chapter Questions

Problem 3MC

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Assume that it costs a company approximately C(x) = 400,000 + 160x + 0.003x² dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. Use it to estimate how fast the cost is increasing when x = 10,000. $ per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) (10,000) = = per smartphone. The exact cost of producing the 10,001st smartphone is $ $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. The marginal cost from (a) is ---Select--- than the average cost from (b). This means that the average cost is ---Select--- Thus, there is a difference of $ at a production level of 10,000 smartphones.
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