A coffee vendor at a popular mall analyzes her records and f

A coffee vendor at a popular mall analyzes her records, and finds that if she sells x cups of coffee in one day, her profit, P (in dollars) is given by P(x) = -0.04 x^2 + 10x - 5 a. How many cups must he sell for maximum profit? b. What is the maximum profit per day?

Solution

Solution:

a)

For P is to be maximum, dp/dx =0

=> dp/dx = d/dx(-0.04x²+10x-5) = 0

=>-0.04×2x + 10 =0

=>-0.08 x = -10

=>x = 125

So he must sell 125 cups per day for maximum profit.

b)

maximum profit per day would be :

P = -0.04(125)+ 10(125)-5

=> P =$ 1250