   Chapter 9.9, Problem 27E ### 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 25-28, cost, revenue, and profit are in dollars and x is the number of units.Suppose that the total revenue function for a product is R ( x ) =   50 x and that the total cost function is C ( x )   =   1900   +   30 x   +  0 .01 x 2 .(a) Find the profit from the production and sale of 500 units.(b) Find the marginal profit function.(c) Find M P ¯  at  x =500 and explain what it predicts.(d) Find P ( 501 )   − P ( 500 ) and explain what this value represents.

(a)

To determine

To calculate: The value of profit on the production and sale of 500 unit. If the total revenue function is represented by R(x)=50x and total cost function is represented by C(x)=1900+30x+0.01x2.

Explanation

Given information:

The total revenue function is represented by R(x)=50x and total cost function is represented by C(x)=1900+30x+0.01x2.

Formula used:

Profit function is given as:

P(x)=R(x)C(x).

Where, R(x) and C(x) represents the revenue function and cost function respectively.

Calculation:

Consider the provided total revenue function and total cost function,

R(x)=50x and C(x)=1900+30x+0.01x2

To calculate the profit, first calculate the profit function by the formula as:

P(x)=R(x)C(x)

(b)

To determine

To calculate: The value of marginal profit function. If the total revenue function is represented by R(x)=50x and total cost function is represented by C(x)=1900+30x+0.01x2.

(c)

To determine

To calculate: The value of marginal profit function at x=500 and also predict the result. If the total revenue function is represented by R(x)=50x and total cost function is represented by C(x)=1900+30x+0.01x2.

(d)

To determine

To calculate: The value of P(501)P(500). If the total revenue function is represented by R(x)=50x and total cost function is represented by C(x)=1900+30x+0.01x2.

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