Question

Profit is the difference between revenue and cost. The revenue, in dollar, of company that manufactures television can be modeled by the polynomial 3x²+180x. The cost,in dollar, of producing the televisions can be modeled by 3x²-160x+300.The variable x is the number of televisions sold. If 150 televisions are sold ,what is the profit?

C)$50,700​

Answer 1

The profit in this case is equal to $50,700.

Explanation:

As the problem stated profit is the difference between revenue and cost, in this case we have:

`revenue(x) = 3x^2 + 180x`

`cost(x) = 3x^2 - 160x + 300`

So the profit will be the difference between these two functions.

`profit(x) = revenue(x) - cost(x)\\profit(x) = 3x^2 + 180x - 3x^2 + 160x - 300\\profit(x) = 340x - 300`

In order to find the profit when 150 televisions are sold we need to make x equal 150.

`profit(150) = 340*150 - 300\\profit(150) = 51000 - 300 = 50700`

The profit in this case is equal to $50,700.