Consider a continuous review inventory model, where the p$.$d$.$f of the demand during lead time follows a uniform distribution over the range of $0$ to $100.$ The annual demand is $600$ units and the cost of each unit is $$20.$ The inventory carrying cost is $$2$ per unit per year and the order cost is $$20$ per order. Based on experience, it is found that a re$-$order level of $80$ units could be optimal. A$)$ What are the optimum order quantity and the implied shortage cost? Assume that shortages are backordered.

b$)$ Solve problem $1$ assuming that shortages result in lost sales and lost sales double the implied shortage cost.