The data related with a store that orders electric generators from a supplier are given below:

Annual demand $($units$)$

$300$

Ordering cost $($S$)$

$3750$

Purchasing cost per generator $($$$)$

$3000$

Shortage cost per generator $($S$)$

$2000$

Annual inventory carrying cost rate

$30\%$

a$)(10$ points$)$ What is the probability that a customer's demand will not be met during a year?

b$)(5$ points$)$ Determine the service level corresponding to the probability calculated in $($a$).$

c$)(5$ points$)$ What will be shortage cost if the store sets its service level as $98\%?$