please answer a and b in handwriting

a$)$ One of the hot sellers for the Wonka Toy store is the Chocolate Factory Board Game. The store

uses a periodic review inventory system. The review period for the board game is $4$ weeks, while

the lead time to obtain the board game is $1$ week. The demand for the board game is normally

distributed with a mean of $200/$week and a standard deviation of $20/$week$.$ The store uses a service

level of $90\%.$ If the on$-$hand quantity in inventory is $50$ units, how much should the store order?

What is the value of the Target inventory and Safety Stock the store is maintaining?

$(15$ points$)$

b$)$ Joe's Coffee Shoppe orders fresh doughnuts each morning. Joe pays $$0\mathrm{.}25$ per doughnut and

sells doughnuts for $$5\mathrm{.}0$a dozen. The leftover doughnuts are salvaged at half the selling price. A

detailed analysis of past data shows that the number of doughnuts sold per day is better described

by a normal distribution, with a mean $30$ dozens and standard deviation $10$ dozens. Now, how

many doughnuts should Joe stock each day?

$(10$ points$)$