# The profit function P ( x ) as a difference of the two functions of x .

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.6, Problem 60E
To determine

## The profit function P(x) as a difference of the two functions of x.

Expert Solution

The value of profit function P(x) is 0.055x0.0000015x2dollars .

### Explanation of Solution

Given:

The price per bumper sticker is 0.150.000002xdollars and the total cost to produce the order is 0.095x0.0000005x2dollars .

The number of ordered stickers is x.

Formula used:

Revenue Formula

Revenue=priceperitem×numberofitemssold (1)

Profit Formula

profit=revenuecost (2)

Calculation:

The price per bumper sticker is 0.150.000002xdollars .

The number of ordered stickers is x.

Substitute 0.150.000002x for price per item and x for number of items sold in equation (1), to find the function R(x) ,

R(x)=(0.150.000002x)×(x)=0.15x0.000002x2

The total revenue is 0.15x0.000002x2dollars .

The total cost of producing the order is 0.095x0.0000005x2dollars .

Substitute 0.15x0.000002x2 for revenue and 0.095x0.0000005x2 for cost in equation (2), to find the profit function P(x) ,

P(x)=(0.15x0.000002x2)(0.095x0.0000005x2)=0.15x0.000002x20.095x+0.0000005x2=0.055x0.0000015x2

Thus, the value of profit function P(x) is 0.055x0.0000015x2dollars .

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