You are the manager of the restaurant in the IKEA furniture store in Canton, Michigan. Over the past eight weeks you have been experiencing some unpredictable demand for the Swedish Meatballs, a signature item on the menu. In some cases, you prepared too many meatballs that were thrown out at the end of the day. In other cases, you ran out of meatballs and had to provide the customers with a $5 voucher to compensate them for the fact that you ran out (and to make sure they come back). Customers always receive 10 meatballs per order. It costs you $0.03 to make a meatball and you sell them for $0.15 each, i.e. a customer pays $1.50 for 10 of them.

Eight weeks ago, you began collecting daily sales data on the meatballs.

Daily Demand

Probability of Demand

(in meatballs)

2000

0.30

2200

0.25

2400

0.15

2600

0.30

a) Suppose you are developing a simulation to determine the optimal stocking level and you ordering decision (in meatballs) is denoted by Q, provide the complete profit function in terms of D, Q, the price and all costs.

b) Using your profit equation from part a, suppose you set Q = 2200, provide the profit in each of the realizations of demand. Hint: you should come up with 4 total profit computations.

c) Using your profit equation from part a, suppose you set Q = 2400, provide the profit in each of the realizations of demand. Hint: you should come up with 4 total profit computations.

d) Multiply each of the profits by the respective probability and determine the expected profit for Q = 2200 and Q = 2400. Based on the expected profit, which order quantity should you select?

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