Solve the following problems using the Decision Analysis. Construct first the decision tree, and thenuse Bayes' Formula to determine the optimal decision.Decision Problems1. The Quano Company is considering the purchase of mineral rights on a piece of propertyfor P1 million. The price includes a seismic test whether the land is of type X or Ygeological formation. The test cannot be done until after the purchase is made.According to reliable information 60% of the land is of type X formation and 40% of thearea is of type Y. If the company decides to drill on the land, it will cost P2.5 million. Itmay hit oil, gas, or a dry well. Drilling experience indicates that the probability of hittingoil is 25% on X formation and 10% on Y formation. The probability of hitting gas is 30%on X formation and 45% on Y formation. The estimated return for an oil well is P5million and from a gas well, P3 million. Should the company purchase mineral rights?

Answered: Solve the following problems using the…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section9.2: Elements Of Decision Analysis

Problem 3P

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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.
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.)
The model in Example 9.3 has only two market outcomes, good and bad, and two corresponding predictions, good and bad. Modify the decision tree by allowing three outcomes and three predictions: good, fair, and bad. You can change the inputs to the model (monetary values and probabilities) in any reasonable way you like. Then you will also have to modify the Bayes rule calculations. You can decide whether it is easier to modify the existing tree or start from scratch with a new tree.
Answer A.2 a-e a-c is in the picture here is d and e d) What is the qually likely decision? e) Develop a decision tree. Assume each outcome is equally likely, then find the highest EMV.
Can you please draw a decision tree and make the decision boxes in square shape and the chances nodes in circular shape thank you
A landlord can either lease for one or two years or sell offices outrightly for K100 million with payoffs as follows: Lease -100 50 150 Sell 100 100 100 The probability of rejecting is 30%, leasing for one year is 50% and for two years 20%. Required: What is the optimal decision strategy if perfect information were available? What is the expected value of perfect information? A decision maker is looking to minimising costs through three alternative decisions a1 , b2 and c3 under two states of nature/events S1 and S2 with S1 having a probability of 30% . For a1 payoffs for s1 K100 million and s2 K540 million For a2 payoff for s1 K150 million and s2 –K50 million For a3 payoff for s1 K350 million and s2 K320 million Required: Find EMV and recommend the course of action Find the…
A graph that helps decision makers use probability theory by showing the expected values of decisions in varying circumstances is known as a(n) a. Gantt chart b. probability curve c. bar graph d. decision tree In the rational model of decision making, evaluation of alternatives a. is the last step. b. should be as objective as possible. c. can only be done with the help of a decision tree. d. is the only step that requires subjective rationality
7. Consider the following decision table, which Joe Blackburn has developed for Vanderbilt Enterprises: States of Nature Decision Alternatives Probability: 0.35 0.25 0.40 Low Medium High A $35 $80 $65 B $85 $50 $70 C $55 $70 $75 D $70 $85 $65 E $70 $75 $85 Part 2 The alternative that provides Blackburn the greatest expected monetary value (EMV LOADING... ) is ▼ D E A B C The EMV for this decision is $_______(enter your answer as a whole number).
What will be Hale’s TV Production’s decision based on the following criteria:a. MAXIMAXb. MAXIMINc. MINIMAX REGRETd. EXPECTED VALUEe. Construct the decision tree for this problem and indicate the decision based on the decision tree analysis.can you pls answer letter a,b,c
1) A decision maker using an exponential utility function would prefer a random payoff with an expected value of X to a certain payoff of X. True False 2) In a decision tree, a circular node indicates a point where a random event occurs. True False 3) The optimistic and conservative approaches to decision making will always give the same result. True False
An optimistic decision-making criterion is sometimes called: a. equally like criterion b. decision making under certainty c. maximin criterion d. maximax criterion
Zaki has been thinking about starting his own petrol station. He’s problem is to decide how large his petrol station should be. The annual return that will be achieved depends on whether the economy is good, fair, or poor. A payoff table has been constructed to illustrate this situation: (Business Quantitative Analysis) Determine using the best investment using the following decision criteria: a) Maximax criterion b) Maximin criterion c) Equally Likely criterion d) Minimax Regret criterion The probabilities of good market, average market, and poor market are 0.4, 0.5, and 0.1 respectively. Construct an expected opportunity loss table. Using minimum EOL as the decision criterion, determine the best alternative

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