Assume that you want to minimize expected outcomes of the givendecisions. Based on the expected monetary values, what is the optimaldecision path?ABCE10%, $9050%$2040%$100$50$45D30% F70%G5%95%50%50%$70$50$70$30$60$30At 'A', choose path to 'E' and if you reach 'F', choose path to $30At 'A', choose path to 'C' and then choose path to $45At 'A', choose path to 'C' and then choose path to 'D'O At 'A', choose path to 'E' and if you reach 'F', choose path to $70

Goal: To minimize the expected outcome of the given decisions.

Answered: Assume that you want to minimize…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 44P: You now have 5000. You will toss a fair coin four times. Before each toss you can bet any amount of...

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You now have 10,000, all of which is invested in a sports team. Each year there is a 60% chance that the value of the team will increase by 60% and a 40% chance that the value of the team will decrease by 60%. Estimate the mean and median value of your investment after 50 years. Explain the large difference between the estimated mean and median.
You now have 5000. You will toss a fair coin four times. Before each toss you can bet any amount of your money (including none) on the outcome of the toss. If heads comes up, you win the amount you bet. If tails comes up, you lose the amount you bet. Your goal is to reach 15,000. It turns out that you can maximize your chance of reaching 15,000 by betting either the money you have on hand or 15,000 minus the money you have on hand, whichever is smaller. Use simulation to estimate the probability that you will reach your goal with this betting strategy.
In this version of dice blackjack, you toss a single die repeatedly and add up the sum of your dice tosses. Your goal is to come as close as possible to a total of 7 without going over. You may stop at any time. If your total is 8 or more, you lose. If your total is 7 or less, the house then tosses the die repeatedly. The house stops as soon as its total is 4 or more. If the house totals 8 or more, you win. Otherwise, the higher total wins. If there is a tie, the house wins. Consider the following strategies: Keep tossing until your total is 3 or more. Keep tossing until your total is 4 or more. Keep tossing until your total is 5 or more. Keep tossing until your total is 6 or more. Keep tossing until your total is 7 or more. For example, suppose you keep tossing until your total is 4 or more. Here are some examples of how the game might go: You toss a 2 and then a 3 and stop for total of 5. The house tosses a 3 and then a 2. You lose because a tie goes to the house. You toss a 3 and then a 6. You lose. You toss a 6 and stop. The house tosses a 3 and then a 2. You win. You toss a 3 and then a 4 for total of 7. The house tosses a 3 and then a 5. You win. Note that only 4 tosses need to be generated for the house, but more tosses might need to be generated for you, depending on your strategy. Develop a simulation and run it for at least 1000 iterations for each of the strategies listed previously. For each strategy, what are the two values so that you are 95% sure that your probability of winning is between these two values? Which of the five strategies appears to be best?
The game of Chuck-a-Luck is played as follows: You pick a number between 1 and 6 and toss three dice. If your number does not appear, you lose 1. If your number appears x times, you win x. On the average, use simulation to find the average amount of money you will win or lose on each play of the game.
Play Things is developing a new Lady Gaga doll. The company has made the following assumptions: The doll will sell for a random number of years from 1 to 10. Each of these 10 possibilities is equally likely. At the beginning of year 1, the potential market for the doll is two million. The potential market grows by an average of 4% per year. The company is 95% sure that the growth in the potential market during any year will be between 2.5% and 5.5%. It uses a normal distribution to model this. The company believes its share of the potential market during year 1 will be at worst 30%, most likely 50%, and at best 60%. It uses a triangular distribution to model this. The variable cost of producing a doll during year 1 has a triangular distribution with parameters 15, 17, and 20. The current selling price is 45. Each year, the variable cost of producing the doll will increase by an amount that is triangularly distributed with parameters 2.5%, 3%, and 3.5%. You can assume that once this change is generated, it will be the same for each year. You can also assume that the company will change its selling price by the same percentage each year. The fixed cost of developing the doll (which is incurred right away, at time 0) has a triangular distribution with parameters 5 million, 7.5 million, and 12 million. Right now there is one competitor in the market. During each year that begins with four or fewer competitors, there is a 25% chance that a new competitor will enter the market. Year t sales (for t 1) are determined as follows. Suppose that at the end of year t 1, n competitors are present (including Play Things). Then during year t, a fraction 0.9 0.1n of the company's loyal customers (last year's purchasers) will buy a doll from Play Things this year, and a fraction 0.2 0.04n of customers currently in the market ho did not purchase a doll last year will purchase a doll from Play Things this year. Adding these two provides the mean sales for this year. Then the actual sales this year is normally distributed with this mean and standard deviation equal to 7.5% of the mean. a. Use @RISK to estimate the expected NPV of this project. b. Use the percentiles in @ RISKs output to find an interval such that you are 95% certain that the companys actual NPV will be within this interval.
A new edition of a very popular textbook will be published a year from now. The publisher currently has 1000 copies on hand and is deciding whether to do another printing before the new edition comes out. The publisher estimates that demand for the book during the next year is governed by the probability distribution in the file P10_31.xlsx. A production run incurs a fixed cost of 15,000 plus a variable cost of 20 per book printed. Books are sold for 190 per book. Any demand that cannot be met incurs a penalty cost of 30 per book, due to loss of goodwill. Up to 1000 of any leftover books can be sold to Barnes and Noble for 45 per book. The publisher is interested in maximizing expected profit. The following print-run sizes are under consideration: 0 (no production run) to 16,000 in increments of 2000. What decision would you recommend? Use simulation with 1000 replications. For your optimal decision, the publisher can be 90% certain that the actual profit associated with remaining sales of the current edition will be between what two values?
3. The manager for a manufacturing company must recommend whether to construct a large plant, construct a small plant or do nothing. He estimates the long-run profits in $ as follows: State of Nature Alternative Good Average Poor Market($) Market ($) Market ($) Construct a 100,000 35,000 -60,000 large plant Construct a 75,000 25,000 -40,000 small plant Do nothing -5,000 0 0 Probability 25% 50% 25% Solve using: A. Expected Opportunity Loss B. Expected Value of Perfect Information
Suppose you want to mine for gold. Your decisions are to build a mine or not, and to hire a geologist or not. If you find gold, you will earn R2 million in profit; if you fail to find gold, you will lose R0.5 million. On the geologist's website, he states he predicts success 50% of the time and failure 50% of the time; when he predicts success, then you are 80% likely to actually succeed; when he predicts failure, then you are 90% likely to actually fail. The geologist costs R0.1 million. You estimate without a geologist you have a 45% chance of success. Use a decision tree to maximize your expected value.
The preference of an agents on lotteries can be represented by an expected utility function u such that u(x) = 3y^1/2 -10. Then the agent is A) not risk averse B) risk loving C) risk neutral D) risk averse E) NOPAC
The Modern Gift Shop prints its own greeting cards. Suppose that the historical record on demand for a Valentine's Day card shows that the demand for the card is governed by the following discrete random variable: Demand 10,000 20,000 40,000 60,000 Probability 0.10 0.35 0.3 0.25 The greeting card sells for $4.00, and the variable cost of producing each card is $1.50, and fixed cost for printing every 100 cards is $15. Leftover cards must be disposed of at a price of $0.20 per card. How many cards should be printed?
Risk-neutral probabilities are always Select one: O equal to atomic prices O negative O less than physical probabilities O equal to physical probabilities O equal to forward atomic prices
The alternatives shown are to be compared on the basis of their present worth values. At an interest rate of 8% per year, the values of n that you should use in the uniform series factors to make a correct comparison by the present worth method are: Alternative(A) Alternative (B) -25,000 -10,000 10,000 First Cost M&O cost/year 3,000 Salvage value 6,000 -2,000 Life 4 O A n 4 years for A and n =4 years for B OB. None of the above O C. n = 4 years for A and n =3 years for B O D. n = 12 years for A and n = 12 years for B

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Assume that you want to minimize expected outcomes of the given decisions. Based on the expected monetary values, what is the optimal pien noth?