Francq Company is a regional distributor of automobile window glass. With the growing level of consumer demand for fuel$-$efficient subcompact cars, management recognizes a need to determine the total inventory cost associated with maintaining an optimal supply of replacement windshields that will fit these vehicles. Francq is expecting a daily demand for $100$ windshields. The purchase price of each windshield is $$200.$

Other costs associated with ordering and maintaining an inventory of these windshields are as follows:

a$.$ The historical ordering costs incurred in the Purchase Order Department for placing and processing orders are shown below:

Year Orders Placed and Processed Total Ordering Costs

$156$ $ $34,440$

$215434,930$

$328035,560$

Management expects the order costs to increase $20\%$ over the amounts and rates experienced during the past three years.

The windshield manufacturer charges Francq a $$104$ shipping fee per order.

A clerk in the Receiving Department receives, inspects, and secures the windshields as they arrive from the manufacturer. This activity requires eight hours per order received. This clerk has no other responsibilities and is paid at a rate of $$15\mathrm{.}00$ per hour. Related variable overhead costs in this department are applied at the rate of $$2\mathrm{.}50$ per hour.

Additional warehouse space will have to be rented to store the new windshields. Space can be rented as needed in a public warehouse at an estimated cost of $$5,000$ per year plus $$5\mathrm{.}00$ per windshield.

Breakage cost is estimated to be $10\%$ of the cost per windshield.

Taxes and fire insurance on the inventory are $$5\mathrm{.}00$ per windshield.

The desired rate of return on the investment