After an initial peak in demand, the demand for iPhone $6$ stabilizes at $3500$ units per week at the Verizon store in Atlanta. The standard deviation of demand is $820$ units. The lead time to reorder iPhones is $4$ weeks, and the P is $2$ weeks. The store manager wants to ensure a service level of $99\mathrm{.}5\%.$

a$.$ What is the safety stock the Verizon store has to keep in order to ensure this service level?

b$.$ What is the target inventory for the iPhone?

c$.$ The store does the inventory review today. It has an on$-$hand inventory of $12,550$ units and there are $7,800$ units in the pipeline inventory. How much should they order?