Return to the automobile manufacturing plant

from Problem $3\mathrm{.}5.$ Suppose nowthat the rate at which the plant uses powerlock

mechanisms

is stochastic and normally distributed, with a mean of $192$ per day $(8$ per hour$)$ and a standard

deviation of $17\mathrm{.}4$ per day. Replenishment orders for powerlock

mechanisms incur a lead

time of $3$ days. If the plant runs out of power locks, it must expedite them from the supplier

at a cost of $$40$ each. Using the EIL approximation for $($r;Q$)$ policies in Section $5\mathrm{.}3\mathrm{.}1,$

find approximate values for r and Q$.$ Also report the expected total cost per week, using

equation $(5\mathrm{.}7).$