Suppose you want to mine for gold. Your decisions are to build a mine or not, and to hire ageologist 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 thetime and failure 50% of the time; when he predicts success, then you are 80% likely to actuallysucceed; when he predicts failure, then you are 90% likely to actually fail. The geologist costsR0.1 million. You estimate without a geologist you have a 45% chance of success. Use a decisiontree to maximize your expected value.

Answered: Suppose you want to mine for gold. Your…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section9.5: Multistage Decision Problems

Problem 19P

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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.
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.
At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is 100, 90, 50, or 10, respectively. After observing the condition of the machine at the beginning of the week, the company has the option, for a cost of 200, of instantaneously replacing the machine with an excellent machine. The quality of the machine deteriorates over time, as shown in the file P10 41.xlsx. Four maintenance policies are under consideration: Policy 1: Never replace a machine. Policy 2: Immediately replace a bad machine. Policy 3: Immediately replace a bad or average machine. Policy 4: Immediately replace a bad, average, or good machine. Simulate each of these policies for 50 weeks (using at least 250 iterations each) to determine the policy that maximizes expected weekly profit. Assume that the machine at the beginning of week 1 is excellent.
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.
An expensive piece of equipment is used in the masking operation for semiconductor manufacture.A capacitor in the equipment fails randomly. The capacitor costs $7.50, but if it burns out while the machine is in use, the production process must be halted. Here the replacement cost is estimated to be $150. Based on past experience, the lifetime distribution of the capacitor is estimated to be Number of Months Probability of of Service Failure 1 .08 2 .12 3 .16 4 .26 5 .22 6…
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
A company is considering whether to develop and market a particular product. There is 40% probability that the research and development department will come up with a viable product, and a 60% probability that the product will be scrapped. The cost of undertaking the research and development is 200 000.
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Texas Petroleum Company is a producer of crude oil that is considering two drilling projects with the following profit outcomes and associated probabilities: Drilling Project, A Profit -$300,000 100,000 500,000 600,000 Probability (percent) 10 60 20 10 Drilling Project, B Profit -$600,000 100,000 300,000 1,000,000 The manager's attitude toward risk is as follows: Profit ($'000) -600 -300 100 U(II) 0.00 0.05 0.20 Note: U(II) stands for utility index of profit. 300 0.30 500 0.45 Probability (percent) 15 25 40 20 600 0.55 1,000 1.00 In making decision under risk, which project will be chosen by the manager of Texas Petroleum Company based on his behaviour toward risk? Also describe the manager's ways of handling decision-making associate with risk. Justify your answers using numerical explanation.
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The company is considering whether or not they should drill the land. The cost of drilling is estimated to be $4 million. The company believes there are three possible findings after drilling the land: dry, wet and gushing. The probabilities for these outcomes are 0.5, 0.3 and 0.2, respectively. If the land is found to be dry, it obviously offers no profit. If the land is wet, it brings a potential profit of $10 million. If gushing, the potential profit from the land is $30 million. Answer the following questions, Q1 and Q2. Q1: Draw a decision tree to show the decision for this company based on the EMV criterion. Nodes and arcs are provided below and you can make more of them by using "copy" and "paste" Q2: The company has the option of using some new technology and equipment combined with seismic survey data to learn the presence of oil (dry, wet or gushing) before drilling the land. However, it requires $2.3 million investment for the technology, equipment, and required analysis. Is…

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