Additional Algo $11-4$ On$-$Order Quantity

A factory orders supplies every $8$ days. The lead time for deliveries is $3$ days. Demand for butter averages $20$ pounds per day with a

standard deviation of $2\mathrm{.}3$ pounds. The holding cost for butter is $$0\mathrm{.}37$ per pound per day. The factory wants to achieve an in$-$stock

probability rate of $99\mathrm{.}87\%$ for butter.

On average, how many pounds of butter will the factory have on order?