Question

Suppose a publishing company estimates that its monthly cost is C(x) = 600x ^ 2 + 300x and its monthly revenue is R(x) = - 0.4x ^ 3 + 700x ^ 2 - 600x + 500 , where xis in thousands of books sold. The profit is the difference between the revenue and the cost What is the profit function, P(x)

Answer 1

Answer:
`P(x)= - 0.4x ^ 3 +100x^2-900x+500`

Explanation:

Given: Monthly cost :
`C(x) = 600x ^ 2 + 300x`

Monthly revenue :
`R(x) = - 0.4x ^ 3 + 700x ^ 2 - 600x + 500`, where x is in thousands of books sold.

Profit = Revenue - Cost

Now , Profit function : P(x) = R(x)-C(x)

`=- 0.4x ^ 3 + 700x ^ 2 - 600x + 500 - ( 600x ^ 2 + 300x )\\\\= - 0.4x ^ 3 + 700x ^ 2 - 600x + 500 -600x ^ 2 - 300x\\\\= - 0.4x ^ 3 +100x^2-900x+500`

Hence,
`P(x)= - 0.4x ^ 3 +100x^2-900x+500`