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?

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?

Answer 1

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.