Question

A magazine company estimates that its monthly cost isC(x) = 700x2 + 400x and its monthly revenue isR(x) = -0.4x3 + 900x2 2002 + 600, where x is in thousands ofmagazines sold. The profit is the difference between the revenue and thecost.What is the profit function, P(x)?A. P(x) = -0.4x3 + 1600x2 + 200x + 600B. P(x) = -0.4x3 + 200x2 – 600x + 600O C. P(x) = 0.4x3 + 200x2 – 600x + 600O D. P(x) = 0.4x3 – 200x2 + 600x – 600

Answer 1

By definition the profite function is the difference between the revenue and the cost, then:

`\begin{gathered} P(x)=R(x)-C(x) \\ =-0.4x^3+900x^2-200x+600-(700x^2+400x) \\ =-0.4x^3+900x^2-200x+600-700x^2-400x \\ =-0.4x^{3^{}}+200x^2-600x+600 \end{gathered}`

Therefore the answer is B.