QUESTION $3$

Weekly demand for a television is normally distributed with mean $55$ and standard deviation $19.$ The lead time from the

plant to your store is $3$ weeks and you order inventory replenishments weekly. You use the order$-$up$-$to model to control

inventory.

Suppose the order$-$up$-$to level is $S=250.$

a$.$ You are preparing to place an order and note that your inventory level is $111$ and you have $78$ televisions on order.

How many televisions will you order? $($Provide your answer as an integer.$)$

b$.$ The following week, your inventory level is $189$ and you have $64$ televisions on order. How many televisions will you

order? $($Provide your answer as an integer.$)$

What order$-$up$-$to level would you choose if you want to achieve a $98\mathrm{.}75\%$ in$-$stock probability? $($Provide your answer

to two decimal places.$)$

Suppose the order$-$up$-$to level is $S=220.$

a$.$ What is your expected on$-$hand inventory? $($Provide your answer to two decimal places.$)$

b$.$ What is your expected on$-$order inventory? $($Provide your answer as an integer.$)$ Please provide complete working for each answer and excel working is require.