Question

The function f(x) = –(x – 20)(x – 100) represents a company’s monthly profit as a function of x, the number of purchase orders received. Which number of purchase orders will generate the greatest profit?

20
60
80
100

Answer 1

The answer is 60

Explanation:

because when you plug in these numbers to the x, 60 is the greatest one.

Answer 2

Let us solve the following problem by substituting each value with x.

FIRST CHOICE
f(x) = -(20-20)(20-100)
= -(0)(-80)
= 0

SECOND CHOICE
f(x) = -(60-20)(60-100)
= -(40)(-40)
= -(-160)
= 160

THIRD CHOICE
f(x) = -(80-20)(80-100)
= -(60)(-20)
= -(-120)
= 120

LAST CHOICE
f(x) = -(100-20)(100-100)
= -(80)(0)
=0

The answers yielded 0, 160, 120, and 0, respectively.
Thus, the answer is 60.