   Chapter 9, Problem 11T ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 19 and 20, suppose a company has its total cost for a product given by C   ( x )   =   200 x   +   10 , 000 dollars and its total revenue given by R ( x ) =   250 x   −   0.01 x 2 dollars, where x is the number of units produced and sold.(a) Form the profit function for this product.(b) Find the marginal profit function.(c) Find the marginal profit when x   =   1000 and then write a sentence that interprets this result.

(a)

To determine

The profit function for the company with revenue function R(x)=250x0.01x2 and cost function C(x)=200x+10000.

Explanation

Given Information:

The revenue function is R(x)=250x0.01x2 dollars and the cost function for the company is C(x)=200x+10000 dollars, where x is the number of units produced and sold.

Explanation:

Consider the provided revenue function and cost function,

R(x)=250x0.01x2 and C(x)=200x+10000

According to the law of finances, the profit function P(x) for a company is the difference between the revenue and the cost functions of the company

(b)

To determine

To calculate: The marginal profit function for the company with revenue function R(x)=250x0.01x2 and cost function C(x)=200x+10000.

(c)

To determine

To calculate: The value of marginal profit when x=1000 and interpret the result.

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