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Assume that it costs Apple approximately C(x) = 25,600 + 100x + 0.01x² dollars to manufacture x 32GB iPods in a day. 1 (a) The averaqge cost per iPod when they manufacture x iPods in a day is given by C(x)= 25600x1. + 100 + 0.0lx (b) How many iPods should be manufactured in order to minimize average cost? 1600 v iPods per day What is the resulting minimum average cost of an iPod? (Give your answer to the nearest dollar.) 276 x dollars Second derivative test: Your answer above is a critical point for the average cost function. To show it is a minimum, calculate the second derivative of the average cost function. C"(x)= 1600 Evaluate C"(x) at your critical point. The result is positive which means that the average cost is concave up at the critical point, and the critical point is a minimum.

Assume that it costs Apple approximately C(x) = 25,600 + 100x + 0.01x² dollars to manufacture x 32GB iPods in a day. 1 (a) The averaqge cost per iPod when they manufacture x iPods in a day is given by C(x)= 25600x1. + 100 + 0.0lx (b) How many iPods should be manufactured in order to minimize average cost? 1600 v iPods per day What is the resulting minimum average cost of an iPod? (Give your answer to the nearest dollar.) 276 x dollars Second derivative test: Your answer above is a critical point for the average cost function. To show it is a minimum, calculate the second derivative of the average cost function. C"(x)= 1600 Evaluate C"(x) at your critical point. The result is positive which means that the average cost is concave up at the critical point, and the critical point is a minimum.

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.CR: Review Problem Set
Problem 50CR
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Assume that it costs Apple approximately C(x) = 25,600 + 100x + 0.01x2 dollars to manufacture x 32GB iPods in a day. + (a) The average cost per iPod when they manufacture x iPods in a day is given by C(x)= 25600x-! + 100 + 0.01xr (b) How many iPods should be manufactured in order to minimize average cost? 1600 V iPods per day What is the resulting minimum average cost of an iPod? (Give your answer to the nearest dollar.) 276 x dollars Second derivative test: Your answer above is a critical point for the average cost function. To show it is a minimum, calculate the second derivative of the average cost function. C"(x)= 1600 Evaluate C"(x) at your critical point. The result is positive which means that the average cost is concave up at the critical point, and the critical point is a minimum.
Transcribed Image Text:Assume that it costs Apple approximately C(x) = 25,600 + 100x + 0.01x2 dollars to manufacture x 32GB iPods in a day. + (a) The average cost per iPod when they manufacture x iPods in a day is given by C(x)= 25600x-! + 100 + 0.01xr (b) How many iPods should be manufactured in order to minimize average cost? 1600 V iPods per day What is the resulting minimum average cost of an iPod? (Give your answer to the nearest dollar.) 276 x dollars Second derivative test: Your answer above is a critical point for the average cost function. To show it is a minimum, calculate the second derivative of the average cost function. C"(x)= 1600 Evaluate C"(x) at your critical point. The result is positive which means that the average cost is concave up at the critical point, and the critical point is a minimum.
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