Question

A company that manufactures model trains uses the function shown to estimate the profits from selling a certain train set.

In this equation, x = the price in dollars of each train set and P(x) = annual profit in thousands of dollars. According to this function, which statement is true?

The annual profit is zero if each train set costs $40.

The annual profit is a maximum if each train set costs $40.

The annual profit is zero if each train set costs $25.

The annual profit is a maximum if each train set costs $10.

Answer 1

The annual profit is zero if each train set costs $40.

Reason: the graph (or function) has zeros at x = 10 and x = 40, so P(x)=0 at those prices. The vertex (maximum) is halfway between the zeros at x = (10+40)/2 = 25, so the maximum is at $25, not at $10 or $40.