Question

The revenue, in dollars, of a company that produces video game systems can be modeled by the expression 5x2 + 2x – 80. The cost, in dollars, of producing the video game systems can be modeled by 5x2 – x + 100, where x is the number of video game systems sold. If profit is the difference between the revenue and the cost, what expression represents the profit?

Profit can be modeled by the polynomial expression

Options:

x+20
x-180
3x+20
3x-180

If 1,000 video game systems are sold, the company’s profit is $

Options:

820
1,020
2,820
3,020

Answer 1

3x-180 and for the second part its 2,820 i just did that part in the assignment

Answer 2

P(x)=3x-180 ; P(1000)=2820

Explanation:

We are given our Revenue function and Cost function . We have to find the Profit function.

Profit = Revenue - Cost

Revenue
`R(x) = 5x^2+2x-80`

Cost
`C(x)=5x^2-x+100`

Profit

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

=
`5x^2+2x-80 -( 5x^2-x+100 )`

=
`5x^2+2x-80 - 5x^2+ x -100 )`

=
`2x-80 +x-100 )`

P(x)=
`3x-180`

Hence this is our profit function.

Now we have to find the profit when the no. of video games represented by x in this , is 1000. In order to do that we replace x by 1000 in P(x)

P(1000) =
`3(1000)-180`

P(1000) =
`3000-180`

P(1000) =
`2820`