Question
A vendor sells Valentine Candy Boxes and wants to raise the selling price. For every twenty-five cents increase, he loses two customers. What price should he sell the Valentine Candy Boxes for to achieve maximum profit?
Answers
Reiny
Let the selling price be k, where k is a constant
let the number of box originally sold be c, where c is a constant
let the number of price increases by n
number sold = c - 2n
selling price = k + 25n
profit = (c-2n)(k + 25n)
= ck + 25cn - 2kn - 50n^2
d(profit)/dn = 0 + 25c - 2k - 100n = 0 for a max of profit
100n = 25c - 2k
n = (25c - 2k)/100
So once you know the initial selling price and the initial numbers sold, you can then find an actual numeric answer.
let the number of box originally sold be c, where c is a constant
let the number of price increases by n
number sold = c - 2n
selling price = k + 25n
profit = (c-2n)(k + 25n)
= ck + 25cn - 2kn - 50n^2
d(profit)/dn = 0 + 25c - 2k - 100n = 0 for a max of profit
100n = 25c - 2k
n = (25c - 2k)/100
So once you know the initial selling price and the initial numbers sold, you can then find an actual numeric answer.