Martin$-$Pullin Bicycle Corp. $($MPBC$),$ located in Dallas, is a wholesale distributor of

bicycles and bicycle parts. Formed in $1981$ by cousins Ray Martin and Jim Pullin, the

firm's primary retail outlets are located within a $400-$mile radius of the distri$-$bution

center. These retail outlets receive the order from Martin$-$Pullin within two days after

notifying the distribution center, provided that the stock is available. However, if an or$-$

der is not fulfilled by the company, no backorder is placed; the retailers arrange to get

their shipment from other distributors, and MPBC loses that amount of business.

The company distributes a wide variety of bicycles. The most popular model, and the

major source of revenue to the company, is the AirWing. MPBC receives all the models

from a single manufacturer overseas, and shipment takes as long as four weeks from

the time an order is placed. With the cost of communication, paperwork, and customs

clearance included, MPBC estimates that each time an order is placed, it incurs a cost

of $$65.$ The purchase price paid by MPBC$,$ per bicycle, is roughly $60\%$ of the suggested

retail price for all the styles avail$-$able, and the inventory carrying cost is $1\%$ per month

$(12\%$ per year$)$ of the purchase price paid by MPBC$.$ The retail price $($paid by the

customers$)$ for the AirWing is $$170$ per bicycle.

MPBC is interested in making an inventory plan for $2011.$ The firm wants to maintain a

$95\%$ service level with its cus$-$tomers to minimize the losses on the lost orders. The

data col$-$lected for the past two years are summarized in the following table. A forecast

for AirWing model sales in the upcoming year $2011$ has been developed and will be

used to make an inventory plan for MPBC$.$