3.6.9 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 andthe 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) = - 0.03x2 +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)The average profit function is

We will find profit function and marginal profit.

Answered: 3.6.9 | bartleby

Math

Calculus

3.6.9

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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Question

3.6.9

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) = - 0.03x2 +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)
The average profit function is

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