
Inventory Cost Problem
Hey guys, just hoping for a hand on this problem that I think may appear on the final for my Calc class. Any tips would be appreciated!
(1 pt) A manufacturer of computers needs 18,000 cases of memory chips each year. Every shipment of memory chips costs 200 dollars. The memory chips have to be stored in a special dustfree environment at an annual cost of 10 dollars per case based on the maximum number of cases on hand at any one time. Assuming justintime inventory management, how many cases of memory chips should be ordered in each shipment in order to minimize the annual inventory costs? You should round off to the nearest case.
I figure the cost is C=200s+10m, s being number of shipments and m being the maximum number of cases in storage, but I don't know where exactly to go from there.
Thanks!

Still stumped by this one, any help is more than welcome. Thanks guys!

If I understand it well, you got the cost correct.
$\displaystyle C = 200s + 10m$
Now, the total number of cases is 18000, and this is equal to the number of cases in each shipment times the number of shipments.
So, you get:
$\displaystyle sm = 18000$
You can substitute s by 18000/m, then find the derivative and solve for m at C' = 0

Seems simple
It appears to me that your problem is actual a really trick question or just a weird one because they give you additional information in the problem that you don't need to use.
It does not specify a frequency of shipment deliveries, so in order to minimize cost, you want to store virtually nothing, or in the case of manufacturing, the bare minimum needed on a daily bases to operate.
18000/365(day in a year) = 49.3 cases are used each day.
Therefore, if you deliver 50 cases per day, you will always be remaining with a small amount left over, and the next day it would be replenished. Since the goal in the problem is to minimize cost of storage, this would be how to do it. Hence the reference to "justintime" inventory management.
It seems like there is missing information to make it a more difficult question then that. The cost of storing is irrelevant, especially since they don't ask for the cost of anything.
Hopefully that helps!
Brendan