$3.$ A company has the following demand forecast: average weekly demand is $2,500$ units, standard deviation of the weekly demand is $122$ units. Purchase price is $$2\mathrm{.}25$ per unit, fixed ordering cost is $$100$ per order, inventory holding cost is $0\mathrm{.}5\%$ of the purchase price per week $(0\mathrm{.}5\%*52=26\%$ per year$),$ leadtime is $1\mathrm{.}5$ weeks. The service level has been chosen such that there will be no stockout during the leadtime with $90\%$ probability. Each unit of backorder incurs $$1$ penalty cost. The continuous review policy is used.

a$.$ Find the order quantity, reorder point, and safety stock $(3$ points$)$

b$.$ Find the expected annual total cost, including fixed ordering cost, inventory holding cost and backorder cost.

c$.$ Find the type II service level $($item fill rate$)(1$ point$)$