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?

Answer 1

F ( x ) = - ( x -20 ) ( x - 100 ) =
= - ( x² - 100 x - 20 x + 2000 )= 
- x² + 120 x - 2000
The greatest profit is when ; f´( x ) = 0
f ´ ( x ) = - 2 x + 120 = 0
2 x = 120,        x = 60
60 purchase orders will generate the greatest profit.