Question

A manufacturer of medical monitoring devices uses 36,000 cases of components per year. The Ordering cost is 54 dollars per shipment and the annual cost of storage is 1.20 per case. The components are used at a constant rate throughout the year and each shipment arrives just as the preceding shipment is being used up. How many cases should be ordered in each shipment to minimize total cost?

Answer 1

Dont you need another number to solve this? I am really confused of how to do this? Thanks!

Answer 2

Assume N cases per shipment.
They use 36000 cases per year.
So the number of shipments per year = 36000/N
It cost $54 per shipment
So for 36000/N shipments, the shipping cost per year = 54 x 36000/N = 1,944,000/N dollars
Storage costs is $1.20 per case and so for storing N cases per shipment the cost is 1.20N

Total cost = shipping cost + storage cost = 1,944,000/N + 1.2N

Does it look correct so far?

Answer 3

We have found Total Cost C as a function of N.
To minimize the Cost C, find the derivative of C with respect to N and set it to 0.
Then solve for N.

Answer 4

C = 1,944,000/N + 1.2N = 1,944,000N^-1 + 1.2N
dC/dN = -1,944,000N^-2 + 1.2 = 0
1,944,000 = 1.2N^2
N^2 = 1,944,000 / 1.2 = 1,620,000
N = 1273

To minimize cost there should be 1273 cases per shipment.

You may want to have input of others for this problem.

Answer 5

Thanks so much! That seems correct

Answer 6

you are welcome.