Problem $2.$ Weekly demand for a product is Binomial$(3,0\mathrm{.}6).$ Weekly overage and underage costs

are h $=3$$ and p $=6$$ per unit. The purchase cost is c $=1$$ per unit, and there is no fixed cost

of purchasing. The order$-$up$-$to level in each period must be in the set $\{0,1,2,3\}.$ The planning

horizon is T $=2$ weeks and the terminal cost at the end of this planning horizon is u$($x$)=$ x$++2$x$.$

We begin week $1$ with x $=2$ units of inventory. The weekly discount factor is $\backslash$gamma $=0\mathrm{.}95.$ Draw a

portion of the probabilistic shortest path network for period $1$ starting with a node corresponding

to inventory x $=2.$ Apply DP to compute and report in a tabular format the optimal cost $\backslash$theta t$($x$)$

and the optimal order$-$up$-$to levels yt$($x$)$ for each week t and each inventory level x