Question

The revenue, in dollars, of a company that makes toy cars can be modeled by the polynomial 3x^2 + 4x – 60. The cost, in dollars, of producing the toy cars can be modeled by 3x^2 – x + 200. The number of toy cars sold is represented by x.

If the profit is the difference between the revenue and the cost, what expression represents the profit?
3x – 260
3x + 140
5x – 260
5x + 140

Answer 1

Hello,

P(x)=3x²+4x-60-(3x²-x+200)=5x-260

Answer C

Answer 2

The expression which represents profit is:

`5x-260`

Explanation:

The number of toy cars sold is represented by: x.

Now, the revenue, in dollars of a company is given by the polynomial function:

`R(x)=3x^2+4x-60`

and the cost, in dollars of producing the toy car is given by the polynomial expression:

`C(x)=3x^2-x=200`

Also, let P(x) denote the profit function.

It is given that:

Profit is the difference between the revenue and the cost.

i.e.

`Profit=R(x)-C(x)\\\\i.e.\\\\P(x)=R(x)-C(x)\\\\i.e.\\\\P(x)=3x^2+4x-60-(3x^2-x+200)`

( Now we know that if the sign before the parentheses is negative then the terms inside the parentheses open up with opposite signs)

i.e.

`P(x)=3x^2+4x-60-3x^2+x-200\\\\i.e.\\\\P(x)=3x^2-3x^2+4x+x-6-200`

( Since, on combining the like terms)

i.e.

`P(x)=5x-260`