Dotz’s Bakery bakes fresh apple pies each morning for sale that day. A pie costs $2.00 to make and sells for $4.00. Any pies left at the end of the day are sold the following day at a discounted price of $1.50. Based on her past experience, the bakery’s manager expects to sell between 10 and 12 pies per day. Based on historical sales records, the bakery manager estimates the probabilities of the different apple pie demand levels as the following:

# of Pies 10 11 12

Probability 0.30 0.35 0.35

(a) Construct the decision tree that can be used to determine how many pies the bakery should bake daily.

(b) Determine the number of pies to bake to maximize the expected daily profits.

(c) Suppose the bakery is uncertain about the probabilities provided in the problem. It is all right with the probability for the demand for 10 pies being 0.30 and does not believe this should be changed. It is not certain about the probabilities for the demand for 11 and 12 pies each being 0.35. What are the probabilities for selling 11 pies and for selling 12 pies that make the expected profit for the 11 pie decision equal to the expected profit for the 12 pie decision?