e$-$stock level for gaskets?

$9\mathrm{.}3($Stocking Latex Gloves$)$ A university health clinic uses exactly $4$ boxes of latex

gloves per week and orders gloves once per week. It costs the clinic $$0\mathrm{.}10$ per week to

hold one box of gloves in inventory. If the clinic runs out of gloves before the end of the

week, they must buy more gloves from a local pharmacy at a cost that is $$0\mathrm{.}50$ greater per

box than the cost their normal supplier charges.

The clinic$$s normal supplier of gloves is quite unreliable. In any period, there is a

$50\%$ chance that the supplier is disrupted and cannot ship any gloves. This probability is

independent of whether the supplier was disrupted in the previous period; that is$,\backslash$alpha $=\backslash$beta $=$

$0\mathrm{.}5.$ What is the optimal base$-$stock level for the clinic to use when ordering gloves?