The management policy of a certain company is to never run out of

stock. The sales department carried out an analysis of a particular

item to evaluate this policy. The demand is deterministic and con$$

stant over time at $625$ units per year. The unit cost of the item is $$50$

independent of the quantity ordered. The cost of placing an order is

$$5\mathrm{.}00$ and the inventory carrying charge is I $=0\mathrm{.}20.$ Units can be

backordered at a cost of $$0\mathrm{.}20$ per unit per week. Calculate the

optimal operating doctrine under the assumption that no stockouts

are allowed, and under the assumption that units can be backordered

at the cost indicated above. What is the dollar loss per year caused

by the no stockout policy if the sales department has correctly esti$$

mated the pertinent parameters?