Question

The revenue, in thousands of dollars, of a new flavor of liquor is given below as function of the number of gallons (in hundreds), x, sold:


`r(x) = 50x - {x}^(2)`
What is the maximum revenue? Use units​

Answer 1

$625,000

Explanation:

The maximum revenue will be found where the derivative of the revenue function is zero.

r'(x) = 50 -2x = 0

50 = 2x

x = 25

When 2500 gallons are sold, the revenue is ...

r(25) = 50(25) -25(25) = (50 -25)(25) = 25(25) = 625 . . . thousands

The maximum revenue is $625,000.