A toy store in a small town of Melbourne receives unitary customer demand for his best selling

products. He decides to control his inventory using $(S,s)$ policy. His orders are delivered within

$LT$ amount of day. The distribution of daily demand is given below.

$Pr\{D_t=k\}=\{\begin{array}{ccc}0& w.p.& 1-p\\ 1& w.p.& p\end{array}$

a$.$ Show that his lead time demand follows Binomial distribution with parmaters LT and

$p$

b$.$ Calculate the distribution of inventory level given that $S=3$ and $s=1.$

c$.$ Calculate the optimum policy parameters for $h=1\mathrm{.}5$ and $b=8.$