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

$2,820

Step-by-step explanation:

In this question, we need to find how much profit the company made.

First, find how much revenue they made using the expression: 5x² + 2x - 80

Since we know they sold 1,000 videogame systems, plug in 1000 into x.

5(1000)² + 2(1000) - 80

Solve:

5(1000)² + 2(1000) - 80

5000000 + 2000 - 80

Revenue: $5,001,920

Since revenue is not the number for profit, we need to find how much it cost to make the 1000 videogame systems. Use the expression: 5x² – x + 100

Plug in 1000 to x.

Solve:

5(1000)² – 1000 + 100

5000000 – 1000 + 100

Cost to make: $4,999,100

Now, to find the profit, we would subtract the cost to make from the revenue. This is represented with the function: P(x) = R(x) - C(x)

P(x) = Profit

R(x) = Revenue

C(x) = Cost

Solve:

5,001,920 - 4,999,100 = $2,820

This means that the company made $2,820 in profit