Question

The revenue for a business, as a function of units produced, s, is

shown below by R(x). C(x) represents the cost of producing x
units. Calculate the profit function and then determine how many
units must be produced for the business to make a profit of
$1680.
R(x) = 292
The revenue
function
The cost function
C(x) = 17x + 504

Answer 1

`P(x) = - 17x-212` --- profit function

Explanation:

Given

`C(x) =17x + 504`

`R(x) = 292`

Solving (a): The profit function

This is calculated as:

`P(x) = R(x) - C(x)`

So, we have:

`P(x) = 292 - 17x - 504`

`P(x) = - 17x+292 - 504`

`P(x) = - 17x-212`

Solving (b):Units to make 1680

`P(x) = - 17x-212`

Substitute 1680 for P(x)

`1680 = -17x - 212`

Collect like terms

`17x= -1680 - 212`

`17x= -1892`

Divide by 17

`x= -111`

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