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Unformatted text preview: Lecture 24 1 Lecture 23, Part II and Lecture 24 Optimization Problems (Sec. 4.4, 4.5) Optimization, Part I (Sec. 4.4) ex. A product has demand function p ( x ) = 64 x and cost function C ( x ) = 0 . 8 x +600, 0 x 4000. Find the production level that will maximize profit. What should the selling price be? Lecture 24 2 Find the production level at which marginal revenue = marginal cost. What is marginal profit at that level? Maximum Profit Lecture 24 3 ex. The cost function for a product is C ( x ) = 1 . 25 x 2 + 40 x + 500. a) Find the production level which will minimize average cost C ( x ). Lecture 24 4 b) What is the minimum average cost? c) Find the marginal cost at the production level where average cost is minimized. Lecture 24 5 Marginal Cost and Minimum Average Cost Lecture 24 6 ex. The position function of a particle moving along a path is given by s ( t ) = 4 t 3 t 4 . a) When is the particle at its farthest distance from the starting point during the first four seconds of travel (the interval [0 , 4])? Lecture 24 7 b) Find the maximum velocity attained by the par ticle during the first four seconds of travel. Lecture 24...
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This note was uploaded on 07/18/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.
 Spring '08
 Smith
 Calculus

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