Assume that it costs a company approximately\[ C(x) = 400,000 + 160x + 0.003x^2 \]dollars to manufacture $ x $ smartphones in an hour.(a) **Find the marginal cost function.**[Text box for answer]Use it to estimate how fast the cost is increasing when $ x = 10,000 $.$ [Text box] per smartphoneCompare this with the exact cost of producing the 10,001st smartphone.The cost is increasing at a rate of $ [Text box] per smartphone. The exact cost of producing the 10,001st smartphone is $ [Text box]. Thus, there is a difference of $ [Text box].(b) **Find the average cost function $ \overline{C} $ and the average cost to produce the first 10,000 smartphones.**\[ \overline{C}(x) = [Text box] \]\[ \overline{C}(10,000) = \$ [Text box] \](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 option] than the average cost from (b). This means that the average cost is [Select option] at a production level of 10,000 smartphones.

Marginal cost is defined as the change in total production resulting from producing an extra unit of…

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 $ per smartphone. The exact cost of producing the 10,001st smartphone is $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) = C(10,000) = $ (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.

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 $ per smartphone. The exact cost of producing the 10,001st smartphone is $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) = C(10,000) = $ (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.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Assume that it costs a company approximately C(x) = 400,000 + 180x + 0.001x² 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 $ per smartphone. The exact cost of producing the 10,001st smartphone is $ Thus, there is a difference of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) C(10,000) $ (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--- O than the average cost from (b). This means that the average cost is ---Select--- O at a production level of 10,000 smartphones.