Response to the following problem:
Pete's Coffee is planning to stock the Melvitta brand espresso maker. Pete's estimates the annual demand for this coffee maker to be 180 units. The machines, which retail for $189 each, are imported from Italy and cost Pete's $95 each. The cost to place an order with Melvitta is $150, and the lead time is an estimated five weeks. Pete's uses a 30% annual holding cost rate for the coffee makers. Pete's is considering using one of two customer satisfaction plans to deal with the possibility of stockouts of the espresso maker. Under the first plan, Pete's will offer backordered customers one free pound of coffee. This will cost $4.25, and Pete's estimates an additional customer goodwill loss of $15 for each week a customer must wait for the espresso maker. Under the second plan, Pete's will offer backordered customers three free pounds of coffee. This will cost $12.75 but will reduce the additional goodwill loss to $3 for each week a customer must wait for the espresso maker.
a. Which customer satisfaction plan should Pete's adopt?
b. What is the optimal order quantity and reorder point under this plan?
c. Using this policy, what is Pete's expected annual profit on the espresso machines?