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Unformatted text preview: MAC 2233/001-006 Business Calculus, Fall 2011 CRN: 81700–81702, 81705, 81716, 81715 Assistants : Matthew Fleeman, Arbin Rai, Tadesse Zerihun, Vindya Kumari, Junyi Tu, Jing- han Meng On Average cost and marginal cost, Exercise 2.4.64 Let the cost function be C = x 3- 15 x 2 + 87 x- 73 , 4 ≤ x ≤ 9 . Then the average cost is AC = C x = x 2- 15 x + 87- 73 x , 4 ≤ x ≤ 9 , and the marginal cost is MC = dC dx = 3 x 2- 30 x + 87 , 4 ≤ x ≤ 9 . If we graph the average cost and the marginal cost together, we get the following diagram: Note that the green graph is for the average cost and the red graph is for the marginal cost. The diagram shows that the average cost is minimized when Average cost = Marginal cost. Let me first give a “heuristical” reasoning for the fact that the average cost is minimized when the average cost equals the marginal cost. Recall that the marginal cost gives the approximate additional cost for making one more unit of the product. Thus, (a) if marginal cost...
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This note was uploaded on 01/02/2012 for the course MAC 2233 taught by Professor Danielyan during the Fall '08 term at University of South Florida.
- Fall '08