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?

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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?

Calculus1
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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.
@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?
It means n multiplied by the factor of 2400 / a and the sum of 50+2

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Oh ok. So in terms of this question, we multiply the shipping cost by n to find the yearly cost?
Exactly!
Alright, thank you!
No Problem!
@hpfan101, sorry to be late for the answer. I believe @Firez has already cleared up your questions.
@mathmate, it's fine!
sorry if I got it wrong OnO

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