A warehouse manager must set up inventory ordering systems for two new

distribution items, $x$ and $Y.$ Item $x$ can be ordered at any time, but item $Y$ can

only be ordered once every three weeks. The company operates $50$ weeks a year

and the weekly demand for both items is normally distributed. The manager has

gathered the following information about the items:

a$.$ When should the manager reorder each item?

b$.$ Compute the order quantity for Item X$.$

c$.$ Compute the order quantity for Item $Y$ if $500$ units are on hand at the time

the order is placed.

d$.$ Compute the optimal order interval for Item Y $($i$.$e$.,$ the current three$-$week

order interval may not be optimal$).$

e$.$ Compute the savings in average inventory carrying costs if Item $Y$ can be

ordered at any time $($rather than once every three weeks$).$