   Chapter 9.9, Problem 28E Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
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 is given by R ( x )   =   46 x and that the total cost function is given by   C ( x ) =   100   +   30 x   +  0 .1 x 2 (a) Find P( 100).(b) Find the marginal profit function.(c) Find M P ¯  at  x =100 and explain what it predicts.(d) Find P( 101) — P( 100) and explain what this value represents.

(a)

To determine

To calculate: The value P(100) when total revenue function is R(x)=46x and total cost function is C(x)=100+30x+0.1x2.

Explanation

Given information:

Total revenue function is R(x)=46x and total cost function is C(x)=100+30x+0.1x2.

Formula used:

Profit function is given as:

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

Calculation:

Consider total revenue function is R(x)=46x and total cost function is C(x)=100+30x+0.1x2.

Profit function is given as:

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

Now substitute the value of R(x) and C(x) in the profit function as,

P(x)=46x(100+30x+0

(b)

To determine

To calculate: The value of marginal profit function when total revenue function is R(x)=46x and total cost function is C(x)=100+30x+0.1x2.

(c)

To determine

To calculate: The value of marginal profit function at x=100 when total revenue function is R(x)=46x and total cost function is C(x)=100+30x+0.1x2.

(d)

To determine

To calculate: The value of P(101)P(100) when total revenue function is R(x)=46x and total cost function is C(x)=100+30x+0.1x2.

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