In a typical periodic$-$review case, it is assumed that the annual demand is $10,000$ units. The cost of making a review is $$10$ and the cost of placing an order is $$25.$ The cost per unit is $$20,$ the carrying cost is $$4$ per unit per year, and the shortage cost is $$10$ per unit independent of duration. It is found that the demand during $+$ is represented by a normal distribution with a mean $10,000(+)$ and a variance $8,000(+).$ Determine the optimal values of $$ and $($the lead time is $4$ months$).$ Assume that shortages are lost sales.