SOLUTION: A milk tea store sells 500 cups per week when it charges Php 80 per cup. It sells 25 cups more per week for each 1.00 decrease in price. The store's revenue is the product of the n

Question 1166955: A milk tea store sells 500 cups per week when it charges Php 80 per cup. It sells 25 cups more per week for each 1.00 decrease in price. The store's revenue is the product of the number of cups sold and the price of each cup. What price should the store charge to maximize it's revenue?
What is the maximum revenue?
Please with complete solving solution.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
revenue initially is 500*80=40,000
let x change in units
so (500+25x)(80-x) needs to be maximized.
This is 40000+1500x-25x^2
the maximum value of this negative quadratic occurs when x=-b/2a, or -1500/-50 or x=30
So 1250 cups at 50 Php or 62500 Php

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