# Math

An electronics firm uses 600 cases of transistors each year. The cost of storing one case for a year is 90 cents, and the ordering fee is \$30 per shipment. How many cases should the firm order each time to keep total cost at a minimum, assuming the transistors are used at a constant rate throughout the year and that each shipment arrives just as the preceding shipment has been used up?

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Total Cost = storage cost + ordering cost + purchase cost

Ordering cost = (Ordering cost per shipment)(# of cases in shipment)
OC = (\$30)(600/x) = 18000/x

Purchasing Cost = (total of cases ordered)(cost per case)
PC = (600)(x)
PC = 600x

Storage Cost = (average # of cases stored)(storage cost per case)
SC = 18000/x(.90) = 16200/x

x would represent cost per case

TC = 16200/x + 18000/x + 600x
TC = 34200/x + 600x
TC = 34,200 + 600x^2

I am even getting close?

I agree on OC, and PC.

However, the cost of storing depends on how long the cases are there before used. One uses 600 cases/yr, so timestored= casesordered/(600case/yr). But these are not there the entire period, the average is 1/2 *x
Sc=1/2 x* x/600 *.90 check my thinking on this: units are
SC= cases*cases/(cases/yr)*dollars/case, so the units work out.

Now add all the costs, and to get min, take the derivative for cost with respect to x, set to zero, and solve for x.

How would you figure out dollars per case?

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