$12\mathrm{.}7$ Daniel$$s Auto Parts is a small wholesale distributor of automobile after$-$market items. For one particular part, an analysis of historical sales resulted in the distribution of daily demand shown below:

Daily Demand Probability

$00\mathrm{.}1770$

$10\mathrm{.}0770$

$20\mathrm{.}3850$

$30\mathrm{.}2731$

$40\mathrm{.}0879$

When a new supply of the part is ordered, the lead$-$time distribution is shown below $($for example, if the lead time is three, the order arrives on the third day after the order is placed$)$:

Lead time $($days$)$ Probability

$30\mathrm{.}10$

$40\mathrm{.}75$

$50\mathrm{.}10$

$60\mathrm{.}05$

Other information obtained from company records includes the following:

Order cost is $$25\mathrm{.}00$ per order.

Back order cost is $$10\mathrm{.}00$ per stockout.

Unit storage cost is $$0\mathrm{.}75$ per day.