the problem using Polya’s Four-Step Problem-Solving Method. A frog is at the bottom of a 21-foot well. Each time the frog leaps, it moves up 3 feet. If the frog has not reached the top of the well, then the frog slides back 1 foot before it is ready to make another leap. How many leaps will the frog need to escape the well? understand the problem devise a plan carry out the plan look back

the problem using Polya’s Four-Step Problem-Solving Method. A frog is at the bottom of a 21-foot well. Each time the frog leaps, it moves up 3 feet. If the frog has not reached the top of the well, then the frog slides back 1 foot before it is ready to make another leap. How many leaps will the frog need to escape the well? understand the problem devise a plan carry out the plan look back

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 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.
Consider the following card game. The player and dealer each receive a card from a 52-card deck. At the end of the game the player with the highest card wins; a tie goes to the dealer. (You can assume that Aces count 1, Jacks 11, Queens 12, and Kings 13.) After the player receives his card, he keeps the card if it is 7 or higher. If the player does not keep the card, the player and dealer swap cards. Then the dealer keeps his current card (which might be the players original card) if it is 9 or higher. If the dealer does not keep his card, he draws another card. Use simulation with at least 1000 iterations to estimate the probability that the player wins. (Hint: See the file Sampling Without Replacement.xlsx, one of the example files, to see a clever way of simulating cards from a deck so that the Same card is never dealt more than once.)
Based on Babich (1992). Suppose that each week each of 300 families buys a gallon of orange juice from company A, B, or C. Let pA denote the probability that a gallon produced by company A is of unsatisfactory quality, and define pB and pC similarly for companies B and C. If the last gallon of juice purchased by a family is satisfactory, the next week they will purchase a gallon of juice from the same company. If the last gallon of juice purchased by a family is not satisfactory, the family will purchase a gallon from a competitor. Consider a week in which A families have purchased juice A, B families have purchased juice B, and C families have purchased juice C. Assume that families that switch brands during a period are allocated to the remaining brands in a manner that is proportional to the current market shares of the other brands. For example, if a customer switches from brand A, there is probability B/(B + C) that he will switch to brand B and probability C/(B + C) that he will switch to brand C. Suppose that the market is currently divided equally: 10,000 families for each of the three brands. a. After a year, what will the market share for each firm be? Assume pA = 0.10, pB = 0.15, and pC = 0.20. (Hint: You will need to use the RISKBINOMLAL function to see how many people switch from A and then use the RISKBENOMIAL function again to see how many switch from A to B and from A to C. However, if your model requires more RISKBINOMIAL functions than the number allowed in the academic version of @RISK, remember that you can instead use the BENOM.INV (or the old CRITBENOM) function to generate binomially distributed random numbers. This takes the form =BINOM.INV (ntrials, psuccess, RAND()).) b. Suppose a 1% increase in market share is worth 10,000 per week to company A. Company A believes that for a cost of 1 million per year it can cut the percentage of unsatisfactory juice cartons in half. Is this worthwhile? (Use the same values of pA, pB, and pC as in part a.)
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?
A survey was conducted to 12 first time voters on their preferred candidate. The results are: BBM, BBM, LR, IM, PL, PL, IM, IM, BBM, BBM, LR, LR. Which statement is true? The Borda score of PL is two points. BBM wins by plurality method. The Condorcet winner is IM. The modes are LR and IM Which of the following is a property of all linear programming problems? alternate courses of action to choose from minimization of some objectives a computer program usage of graphs in the solution
There are often disputed charges on a guest's folio (bill). Some are legit, for example room service billed the wrong room. However, how would you handle the following guest disputes and why: 1-The guest disputes $200 in phone charges because he thought it was a toll-free number. 2-The guest disputes paying $30 for parking because they feel it is unreasonable, especially when the hotel isn't even full and parking is outside. 3-The guest objects to the room service charge because the food was awful and they didn't finish it.
Which of the following statements is correct regarding the EMH form? Select one: None of the answers are correct If the market is weak-form efficient, then it is also semistrong and strong-form efficient. If the market is semistrong form efficient, then it is also strong form efficient If a market is strong-form efficient, it is also semistrong and weak form efficient If the market is strong-form efficient, it is also semistrong but not weak-form efficient
Gotham City has 10,000 streetlights. City investigatorshave determined that at any given time, an average of 1,000lights are burned out. A streetlight burns out after an averageof 100 days of use. The city has hired Mafia, Inc., to replaceburned-out lamps. Mafia, Inc.’s contract states that thecompany is supposed to replace a burned-out street lamp inan average of 7 days. Do you think that Mafia, Inc. is livingup to the contract?
Louisiana is busy designing new lottery scratch-off games. In the latest game, Bayou Boondoggle, the player is instructed to scratch off one spot: A, B, or C. A can reveal "Loser," "Win $5," or "Win $25." B can reveal "Loser" or "Take a Second Chance." C can reveal "Loser" or "Win $600." On the second chance, the player is instructed to scratch off D or E. D can reveal "Loser" or "Win $5." E can reveal "Loser" or "Win $15." The probabilities at A are 0.70, 0.19, and 0.11. The probabilities at B are 0.70 and 0.30. The probabilities at C are 0.997 and 0.003. The probabilities at D are 0.4 and 0.6. Finally, the probabilities at E are 0.91 and 0.09. Draw the decision tree that represents this scenario. Use proper symbols and label all branches clearly. Calculate the expected value of this game. Choose the correct decision tree below. O A. В. Loser (0.70) Win $5 (0.19) Loser (0.997) Win $5 (0.00). Win $25 (0.11) Win $600 (0.003) 25 600 Loser (0.70) Loser (0.70) Loser (0.4) Loser (0.4) 1 1…
Consider Bruno who manages an underwriting team in an insurance firm. Recently, the management of Bruno’s firm informed him of their decision to create a new risk assessment team, consisting of data scientists with machine learning expertise, and reduce the size of Bruno’s underwriting team. Bruno’s underwriting team will now work with the new risk assessment team in order to determine whether to provide insurance to applicants Use the model of a firm’s technology choice and graphically illustrate the management’s restructuring decision in a diagram with isocost curves. Your diagram should have the amount of human intelligence on the horizontal axis and the amount of artificial intelligence on the vertical axis. Fully label your diagram. Note that there are no actual numbers given in this question: you may make them up or simply use appropriate notations. Briefly explain the key information of your diagram.
Which of the following is true? a)The maximin criterion is an approach in Optimization under uncertainty which finds a solution that has the best possible payoff. b)The maximin criterion is an approach in Optimization under uncertainty which finds a solution with the best worst possible payoff. c)A risk profile represents the probability distribution of uncertain inputs. d)Decision tree is a method to solve any optimization problem when the outcomes are subject to uncertainty.
No probabilities are known for the occurrence of the nature states. Compare the solutions obtained by each of the following criteria: Maximin (Minimax)