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) = -0.05x² + 50x + 110, p(x) = 200, a = 500 a. Find the profit function P. The profit function is P(x) = .

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) = -0.05x² + 50x + 110, p(x) = 200, a = 500 a. Find the profit function P. The profit function is P(x) = .

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 88E

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