Problem $3$

In a P system, the lead time for a box of weed$-$killer is $2$ weeks and the review period is $1$ week. Demand during the protection interval averages $218$ boxes, with a standard deviation of $40$ boxes.

$($a$)$ What is the cycle$-$service level when the target inventory is set at $300$ boxes?

$($b$)$ In the fall season, demand for weed$-$killer decreases but also becomes more highly variable. Assume that during the fall season, demand during the protection interval is expected to decrease to $180$ boxes, but with a standard deviation of $50$ boxes. What would be the cycle$-$service level if management keeps the target inventory level set at $300$ boxes?