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. Complete parts (a) through (d) below. C(x) = - 0.03x? + 50x + 100, p(x) = 100, a = 500 a. Find the profit function P. The profit function is P(x) = 0.03x + 50x - 100 b. Find the average profit function and marginal profit function. P(x) = .03x + 50 100 The average profit function is The marginal profit function is dP = .06x + 50. xp c. Find the average profit and marginal profit if x = a units have been sold. The average profit if x = a units have been sold is $. (Type an integer or a decimal.)

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. Complete parts (a) through (d) below. C(x) = - 0.03x? + 50x + 100, p(x) = 100, a = 500 a. Find the profit function P. The profit function is P(x) = 0.03x + 50x - 100 b. Find the average profit function and marginal profit function. P(x) = .03x + 50 100 The average profit function is The marginal profit function is dP = .06x + 50. xp c. Find the average profit and marginal profit if x = a units have been sold. The average profit if x = a units have been sold is $. (Type an integer or a decimal.)

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.4: Average Rate Of Change Of A Function

Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

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