A medical store sells the wheelchairs from Wheelies. Orders are placed weekly to the Wheelies distributor and the lead-time to receive an order is 2 weeks. If there are some wheelchairs in stock when a customer comes to the store, he or she buys it on the spot. If not, the customer pays for it in full, then is invited to put his or her name on a waitlist. Upon receiving a shipment from the distributor, the store employee first sets aside a number of wheelchairs equal to the number of names on the waitlist and notifies the customers on the waitlist that their wheelchair is ready for pickup. After these wheelchairs have been put aside, the rest of the shipment is put on the shelves inside the store. Assume that every customer who wants a wheelchair is willing to wait for it if it is not in stock and none of them cancels their purchase before receiving it. The discrete demand is in the table below.

Demand	Probability	Expected Sales	Expected Leftover Inventory	Expected ProfitInventory
9	0.08
11	0.12
13	0.22
16	0.28
18	0.18
22	0.12

(a) Suppose the store chooses an order-up-to level of 40, what is the expected inventory level expected on-hand inventory, expected number of backorders, and expected on-order inventory?

(b) Suppose the store chooses an order-up-to level of 40, what is the probability that there are no names on the waitlist at the end of a given week?

(c) Suppose the store chooses an order-up-to level of 40, which proportion of customers leave the store without their wheelchair and have to come back later to pick it up?

(d) Find the order-up-to level that ensures that the store will only stock out at the end of a week 15% of the time.

(e) Suppose it costs the wheelchair store $2 per wheelchair left in stock at the end of the week (because the store employee has to take them one by one into a secure location for storage over the weekend). Also, suppose that every customer who puts their name on the waitlist for a wheelchair gets a $10 discount. The selling price of the wheelchair is $1800. The store purchases them from the distributor for $1650 a piece. What order-up-to level would you recommend they use? Compute the expected weekly cost associated with this order-up-to level and compare it to the cost of having an order-up-to level of 40.

(f) (Challenging - continuing from (e)) Suppose that store has a high-yield savings account with an interest rate of 0.2% a week. Every available dollar the store has is put on this account. How would this change your answer to (e)? Explain.