# What is the optimum order size and minimum inventory cost in the following case:A retailer of motorized bicycles has examined cost data and has determined a cost function which expresses the annual...

What is the optimum order size and minimum inventory cost in the following case:

A retailer of motorized bicycles has examined cost data and has determined a cost function which expresses the annual cost of purchasing owning and maintaining inventory as a function of the size (number of units) of each order it places for the bicycles. The cost function is C= f(q) = 4860/q + 15q + 750,000 where C equals annual inventory cost, stated in dollars and 'q' equals the number of cycles order each time the retailer replenishes the supply.

i. Determine the order size which minimizes annual inventory cost.

ii. What is minimum annual inventory cost expected to equal?

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### 1 Answer

The cost function for the annual cost of purchasing owning and maintaining inventory as a function of the number of units ordered is C= f(q) = 4860/q + 15q + 750000 where C equals annual inventory cost, stated in dollars and 'q' equals the number of cycles ordered each time the retailer replenishes the supply.

To find the order size that minimizes inventory cost solve: f'(q) = 0

-4860/q^2 + 15 = 0

=> q^2 = 4860/15 = 324

=> q = 18

The minimum annual inventory cost is f(18) = 750540

**An order size of 18 minimizes inventory cost and the minimum value is $750540**