Question

Suppose a granola bar company estimates that its monthly cost is C(x) = 500x2 + 400x and its monthly revenue is R(x) = -0.6x3 + 800x2 300x + 600, where x is in thousands of granola bars sold. The profit is the difference between the revenue and the cost. What is the profit function, P(x)?

Answer 1

The profit is defined as the difference between the revenue and the cost. So, it would be P=R-C. Now, considering that R(x) = -0.6x3 + 800x2 300x + 600 and C(x) = 500x2 + 400x we get

`P(x)=-0.6x^3+800x^2-300x+600-(500x^2+400x)`

To simplify averything, we group the numbers by powers of x, we get

`P(x)=-0.6x^3+(800-500)x^2+(-400-300)x+600`

since 800-500=300 and -400-300=-700 we get that

`P(x)=-0.6x^3+300x^2-700x+600`

which is option B.