Example $(2)$: Demand for a chemical at a manufacturing plant can be approximated by a Normal distribution with a mean of $21$ litres per week. The standard deviation of demand per week is $3\mathrm{.}5$ litres. The plant sources the chemical from a local distributer. The plant manager desires a lead time service level of $90$ percent. He has estimated the holding cost per litre to be $$0\mathrm{.}1$ per year and the cost of an order to be $$5.$ Lead time from the distributer is $1$ week. The plant operates seven days a week and $52$ weeks per year.

Find the optimum order quantity.

Determine the reorder point consistent with the desired lead time service level.

Draw a graph of inventory level in a cycle $($indicating ROP and safety stock$).$