A company determined that for each $1 increase in the price of their product, the number of items sold will decrease by 2. Their predicted weekly profit with a

price increase of x dollars is represented by the function

f(x)= – 2x2+20x +150.

By how many dollars

should they increase the price of their product to

maximize their weekly profits?

15

200

150

5

To have maximum profit, the price must be increased by 5,

Step-by-step explanation:

Given that the price increase function is:

f(x) = -2x² + 20x + 150,

For maximum profit, then f(x) = 0.

Putting f(x) = 0, we have

-2x² + 20x + 150 = 0

Or

x² - 10x - 75 = 0

(x + 5)(x - 15) = 0

x = -5

Or

x = 15

Again, differentiating f(x) and equating to zero, we have

-4x + 20 = 0

4x = 20

x = 20/4

= 5

To have maximum profit, the price must be increased by 5,