Central Hydraulic Supply

The Central Hydraulic Supply Company is a distributor of hydraulic supplies in the Midwest. Central handles standard fittings, tubing, and similar items. Generally Central carries an entire product line for each manufacturer it represents providing local stock for rapid delivery to customers. The parts that Central stocks are mainly used in the maintenance of large construction equipment. The company operates $52$ weeks per year.

The company reviewed the cost of preparing and processing a requisition, preparing a purchase order, and making necessary record changes. This was estimated to be $$50$ per order.

One part that Central stocks is a small hydraulic fitting. Central sells about $20,500$ of these fittings per year $($the fitting is purchases for $$14$ and sells for $$19).$ The manufacturer from whom Central buys the fitting does not offer any quantity discount. The manufacturer is located about $1,500$ miles away and the fittings are shipped to Central by truck. They all arrive at once.

The annual per unit inventory holding cost is $20\%$ of the item$$s value.

What is the order quantity that minimizes total annual cost of inventory?

$855\mathrm{.}7$

$825$

$875$

$853\mathrm{.}9$