QUESTION $22(10$ points$)-$ Fixed$-$Quantity Inventory Systems $($FQS$)$

Comfy$5$hoes is an online retaller which carries varlous shoe lines. For simplicity, we are only

interested in the number of palrs of shoes $($the unit is a palr of shoes$),$ not in differences

amongst lines and sizes. The company uses a fixed$-$quantity Inventory system $($FQS$)$ to manage

thelr stock. Following is key Information elther current or averaged over years of operations:

Backorders happen because of shortages in certain sizes. A restock order would include all sizes.

You would need to show equations, steps, and the final results with units for full credits. Time

units should be carefully treated. Goods quantitles should be rounded up to whole numbers.

$($a$)[2]$ Find the Economic Order Quantity $($EOQ$)($rounded up to a whole number$).$ Find the

average total annual cost $($TAC$)$ for the EOQ $(2$ decimal places$).$

$($b$)[1]$ Given the EOQ, find the average number of orders made in a year $(2$ decimal places$).$

What is the average time between orders $($In days with $2$ decimal places$)?$

$($c$)[1]$ Find the current inventory position $($IP$).$

$($d$)[3]$ Find the reorder point without safety stock $R(AD).5$tate the ordering rule. Based on the

current IP$,$ determine if the company would make an order and state the order quantity. Sketch

the normal demand distribution In the lead time to lllustrate the service level. Then, loosely

sketch how the system would operate over time $($movements of Ip over time$).$

$($e$)[3]$ Find the reorder point with safety stock $R(5T).$ State the ordering rule. Based on the

current IP$,$ determine if the company would make an order and state the order quantity. Sketch

the normal demand distribution In the lead time to Illustrate the service level. Then, loosely

sketch how the system would operate over time $($movements of IP over time$).$

Hint: Use the following table to find the $z-$value corresponding to the desired service level.