Problem $3(25$ points$)$

An engineer has decided to pursue ordering option for a

particular item on an as needed basis as opposed to stocking it$.$

To stock the item, inventory inspection costs $$500$ annually. The

cost to place an order is estimated at $$125.$ For the ordering

option, there is an additional $$85$ special delivery charge per

order. Demand for the $$20$ item is $2,300$ units per year. The

annual holding cost rate is $40\%$ of the item price.

a$)$ Calculate range of the order quantity that will make it

economical to order this item every time.

b$)$ If the engineer decides to stock the item what is the order

quantity that is economical.

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