An electronic store needs to order a total of 2400 CD players over the course of a year. It will receive them in several shipments, each containing an equal number of CD players. The shipping costs are as follows: $50 for each shipment, plus a one-time yearly fee of $2 for each CD player in a single shipment. What size should each shipment be in order to minimize yearly shipping costs?

Question

mathmate · Answer

Let there be n shipments having equal shipping quantities of players equal to 2400/n.
Minimum number of shipments per year,  n $\ge$ 1
Cost of each shipment = 50+2(2400/n)
Total yearly cost, C = n(50+2(2400/n)) =50n + 4800
Find the smallest value of n that will minimize the cost using the above equation.

hpfan101 · Answer

@mathmate: Thank you! I understand everything except for the part where you have the variable "n" in front of the (50+2(2400/n). Why do we need to have it there?

anonymous · Answer

It means n multiplied by the factor of 2400 / a and the sum of 50+2

hpfan101 · Answer

Oh ok. So in terms of this question, we multiply the shipping cost by n to find the yearly cost?

anonymous · Answer

Exactly!

hpfan101 · Answer

Alright, thank you!

anonymous · Answer

No Problem!

mathmate · Answer

@hpfan101, sorry to be late for the answer.  I believe @Firez has already cleared up your questions.

hpfan101 · Answer

@mathmate, it's fine!

anonymous · Answer

sorry if I got it wrong OnO