Suppose that the total cost (in dollars) for a product is given by C(x) = 1300 + 160 ln(2x + 1) where x is the number of units produced. (a) Find the marginal cost MC function. MC = 320 · 1 / (2x + 1) (b) Find the marginal cost when 160 units are produced. (Round your answer to the nearest cent.) $ 1.00 Interpret your result. This is the total cost of producing 160 units. This is the total profit from producing 160 units. The profit from the next unit will be approximately this amount. 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 of the marginal cost function? MC ? 0 MC ? 0 MC < 0 MC = 0 MC > 0 Does it apply in this problem? Yes No
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So, we need to find the derivative of C(x) = 1300 + 160 ln(2x + 1). Using the chain rule, the derivative of ln(2x + 1) is 1/(2x + 1) * 2 = 2/(2x + 1). Show more…
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Suppose that the total cost (in dollars) for a product is given by C(x) = 1300 + 160 ln(2x + 1), where x is the number of units produced. (a) Find the marginal cost MC function. MC = 320 * (1 / (2x + 1)) (b) Find the marginal cost when 160 units are produced. (Round your answer to the nearest cent.) $ 1.00 Interpret your result. 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 of the marginal cost function? MC > 0 Does it apply in this problem? Yes
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