Explanation Given information: Marginal cost for a company is given by c ′ ( q ) = q 2 − 16 q + 70 dollars/unit Where q is the quantity produced and C ( 0 ) = 500 Concept used: Cost function C ( x ) gives the cost of producing x units of a good. Marginal cost M C ( x ) gives the cost of producing one additional unit after x units. Total cost of producing b units = fixed cost + total variable cost The total cost is equals to sum of fixed cost and total variable cost. Calculation: Consider the following marginal cost function. M C ( q ) = C ' ( q ) = q 2 − 16 q + 70 And C ( 0 ) = 500 Evaluate the anti-derivative of the marginal cost function, as follows. C ( q ) = ∫ ( q 2 − 16 q + 70 ) d q = q 3 3 − 16 q 2 2 + 70 q + C = q 3 3 − 8 q 2 + 70 q + C Now C ( 0 ) = 500 , gives C ( q ) = q 3 3 − 8 q 2 + 70 q Thus, variable cost is q 3 3 − 8 q 2 + 70 q

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Question

Chapter 5.5, Problem 10P

To determine

To find the total cost with totalvariable cost and fixed cost.

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Chapter 5.5, Problem 9P

Chapter 5.5, Problem 11P

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Knowledge Booster

To find the total cost with totalvariable cost and fixed cost.

Solution Summary: The author evaluates the anti-derivative of the marginal cost function.

To find the total cost with totalvariable cost and fixed cost.

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Chapter 5 Solutions