BOOKY is a bookstore that sells Decision Analysis (DA) textbooks to students. The demand for the DA textbooks is uncertain and depends on the retail price that BOOKY sells the textbook at. The probability distribution of this demand can be assumed from past sales data. 1. At the beginning of each semester, BOOKY can order 60, 80, or 100 copies of the book from the publisher, each with differing discounts per book. The ordering costs are listed in the following table. Number of Books Ordered 60 80 100 Ordering Costs 6100 7700 9100 2. BOOKY can either sell the book at the retail price ($130 per copy) or offer a 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 irrecoverable There are two decision variables in this decision problem: the ordering quantity and the selling price of the textbook. a) If BOOKY is allowed to 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 BOOKY through decision tree analysis. (You need to submit your decision tree drawn) b) Following (a), BOOKY is unsure about the estimated demand distribution for the textbook when the selling price is $130. Hence, BOOKY 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 Z. Find the range of Z in which the optimal decision made in (a) will not change. PLEASE HELP!
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Q2. BOOKY is a bookstore that sells Decision Analysis (DA) textbooks to students. The demand for the DA textbooks is uncertain and depends on the retail price that BOOKY sells the textbook at. The probability distribution of this demand can be assumed from past sales data.
1. At the beginning of each semester, BOOKY can order 60, 80, or 100 copies of the book from the publisher, each with differing discounts per book. The ordering costs are listed in the following table.
| Number of Books Ordered | 60 | 80 | 100 |
| Ordering Costs | 6100 | 7700 | 9100 |
2. BOOKY can either sell the book at the retail price ($130 per copy) or offer a 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 irrecoverable
There are two decision variables in this decision problem: the ordering quantity and the selling price of the textbook.
a) If BOOKY is allowed to 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 BOOKY through decision tree analysis. (You need to submit your decision tree drawn)
b) Following (a), BOOKY is unsure about the estimated demand distribution for the textbook when the selling price is $130. Hence, BOOKY 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 Z. Find the range of Z in which the optimal decision made in (a) will not change.
PLEASE HELP!
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