Question

The price received for a bicycle is given by the equation b = 100 – 10x2, where x is the number of bicycles produced, in millions.

It costs the company $60 to make each bicycle.

What is the profit function for the company?

P = –10x2 – 60x + 100

P = –10x3 + 40x

P = – 10x2 + 40

Answer 1

Revenue = price × quantity = (100 − 10x^2)·x = 100x − 10x^3.
Cost = $60 per bicycle → 60x.
Profit P = revenue − cost = (100x − 10x^3) − 60x = 40x − 10x^3.

So P = −10x^3 + 40x (option B).