$5\mathrm{.}3(($r;Q$)$ for Automobile Components$)$ 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. Find r and Q using each of the methods below. Also report the

expected total cost per week, using equation $(5\mathrm{.}7).$

a$)$ The EIL approximation.

b$)$ The EOQB approximation.

c$)$ The EOQ$+$SS approximation.

d$)$ The lossfunction

approximation.

e$)$ Algorithm $5\mathrm{.}2$ for exact optimal values of r and Q$.$