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.