Question

A cereal company estimates that its monthly cost is

C(x) = 400x2 + 300x and its monthly revenue is
R(x) = -0.6x3 + 900x2 – 400x + 700, where x is in thousands of
boxes sold. The profit is the difference between the revenue and the cost.
What is the profit function, P(x)?

Answer 1

P(x)= -0.6x^3 + 500x^2

Explanation:

given data

monthly cost

C(x) = 400x^2 + 300x

revenue is

R(x) = -0.6x^3 + 900x^2 – 400x + 700,

where x is in thousands of boxes sold.

we know that the profit is the difference between the revenue and the cost.

therefore P(x)=R(x)-C(x)

P(x)= -0.6x^3 + 900x^2 – 400x + 700-(400x^2 + 300x )

P(x)= -0.6x^3 + 900x^2 – 400x + 700-400x^2 - 300x

P(x)= -0.6x^3 + 500x^2