Austin is the a bookstore that sells Decision Analysis (DA) textbooks to students. The retail price of the DA textbook is $130 per copy and the demand for the DA textbooks is uncertain. However, the past sales data can provide a probability distribution estimate of the demand for the DA textbooks to determine the order quantity of the DA textbooks.

1. At the beginning of each semester, Austin can order 60, 80, or 100 copies of the book from the publisher. Moreover, the publisher offers quantity discount. For Austin, the ordering costs under different ordering quantities are listed in the following table.

# of the books ordered Ordering costs

60 $6100

80 $7700

100 $9100

2. Austin can either sell the book at the retail price ($130 per copy) or offer 10% discount ($117 per copy). The demand distributions under different selling prices are listed in the following tables.

The demand distribution for the textbook when the selling price is $130 per copy.

Demand Probability

70 0.6

90 0.4

The demand distribution for the textbook when the selling price is $117 per copy.

Demand Probability

80 0.15

100 0.85

3. Any unmet demand for the textbook will be lost.

There are two decision variables in this decision problem: the ordering quantity and theselling price of the textbook.

a) Form decision tree for this decision problem.

b) Solve your decision tree model and find the optimal ordering quantity and selling price of the textbook for Austin.

c) If Austin can return unsold textbooks to the publisher for a refund of $80 per copy, find the optimal ordering quantity and selling price of the textbook for Austin.

d) Following (c), Austin has doubt about the estimated demand distribution for the textbook when the selling price is $130. Hence, Austin wants to conduct a sensitivity analysis to understand the impact of uncertainty in this demand distribution. Suppose that the probability that the demand for the textbook is 70 is