Problem $20-23($Algo$)$

$8\mathrm{.}5$ points

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Gentle Ben's Bar and Restaurant uses $7,200$ quart bottles of an imported wine each year. The effervescent wine costs $$9$ per bottle and is served only in whole bottles because it loses its bubbles quickly. Ben figures that it costs $$25$ each time an order is placed, and holding costs are $40$ percent of the purchase price. It takes six weeks for an order to arrive. Weekly demand is $144$ bottles $($closed two weeks per year$)$ with a standard deviation of $40$ bottles.

Ben would like to use an inventory system that minimizes inventory cost and will provide a $99$ percent service probability.

a$.$ What is the economic quantity for Ben to order? $($Round your answer to the nearest whole number.$)$

Economic order quantity

bottles

b$.$ At what inventory level should he place an order? $($Use Excel's NORMSINV$()$ function to find the correct critical value for the given $-$level. Do not round intermediate calculations. Round $"z"$ value to $2$ decimal places and final answer to the nearest whole number.$)$

Inventory level

bottles