Problema Solution
A popular designer purse sells for $500 and 45,000 are sold a month. The company did some research and realized that for each $20 decrease in price, they can sell 5000 more purchases per month. How much should the company charge for the purse so they can maximize monthly revenues?
Answer provided by our tutors
let
x = the number of $20 decreases in price
the monthly revenues R will be:
the new price * the total number of purses sold
R = (500 - x*20)*(45,000 + x*500)
R = - 10^4 x^2 + x (- 9*10^5 + 25*10^4) + 225*10^5
R = - 10^4 x^2 - x 65*10^4 + 225*10^5
R = (10^5) * ( - x^2 + 16x + 225)
R is negative quadratic function of x and has a maximum
R = 289 * 10^5 for x = 8
the new price of the purse will be
500 - x*20 = 500 - 8*20 = $340
The company should charge $340 for a purse in order to maximize monthly revenues.