As an operations manager, you have learned that average weekly demand is $48$ units per week with a standard deviation of $8$ units. You believe that your service level should be $94$ percent. Lead time is two weeks. You do an inventory review every Friday to place an order.

a$)$ Determine the required safety stock and the target $($Max$)$ inventory level.

b$)$ It$$s Friday and you are about to place a replenishment order. Now the inventory level is $100$ units. How much do you have to order?