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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)

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JeanaShupp

Answer: [tex]P(x)= - 0.4x ^ 3 +100x^2-900x+500[/tex]

Step-by-step explanation:

Given: Monthly cost : [tex]C(x) = 600x ^ 2 + 300x[/tex]

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

Profit = Revenue - Cost

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

[tex]=- 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[/tex]

Hence, [tex]P(x)= - 0.4x ^ 3 +100x^2-900x+500[/tex]

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