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]
