43-46. Average and marginal profit Let C(x) represent the cost of producing x items and p(x) be the sale price per item if x items are sold. The profit P(x) of selling x items is P(x)=xp(x)-C(x) (revenue minus costs). The average profit per item when x items are sold is P(x)/x and the marginal profit is dp/dx. The marginal profit approximates the profit obtained by selling one more item, given that x items have already been sold. Consider the following cost functions C and price functions p. a. Find the profit function P. b. Find the average profit function and the marginal profit function. c. Find the average profit and the marginal profit if x = a units are sold. d. Interpret the meaning of the values obtained in part (c). 43. C(x) =-002x² +50x+100, p(x) = 100, a = 500

43-46. Average and marginal profit Let C(x) represent the cost of producing x items and p(x) be the sale price per item if x items are sold. The profit P(x) of selling x items is P(x)=xp(x)-C(x) (revenue minus costs). The average profit per item when x items are sold is P(x)/x and the marginal profit is dp/dx. The marginal profit approximates the profit obtained by selling one more item, given that x items have already been sold. Consider the following cost functions C and price functions p. a. Find the profit function P. b. Find the average profit function and the marginal profit function. c. Find the average profit and the marginal profit if x = a units are sold. d. Interpret the meaning of the values obtained in part (c). 43. C(x) =-002x² +50x+100, p(x) = 100, a = 500

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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