Exhibit 20-2Below is a payoff table involving three states of nature and two decision alternatives. Decision States of Nature Alternative s1 s2 s3 A 80 45 –20 B 40 50 15 P(s1) = .1, P(s2) = .6, and P(s3) = .3.Refer to Exhibit 20-2. The expected value of the best alternative equals _____. a. 12 b. 38.5 c. 29 d. 105
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Below is a payoff table involving three states of nature and two decision alternatives.
Decision | States of Nature | ||
Alternative | s1 | s2 | s3 |
A | 80 | 45 | –20 |
B | 40 | 50 | 15 |
P(s1) = .1, P(s2) = .6, and P(s3) = .3.
Refer to Exhibit 20-2. The expected value of the best alternative equals _____.
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- What information does a decision maker need in order to perform an expected-value analysis ofa problem? What options are available to the decision maker if the probabilities of the states ofnature are unknown? Can you think of a way you might use sensitivity analysis in such a case?The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars): Decision State of Nature Alternative Low Demand (S1) Medium Demand (S2) High Demand )S3) Manufacture, d(1) -20 40 100 Purchase, d(2) 10 45 70 The state-of-nature probabilities are P s1= 0.35, P s2= 0.35, and P s3= 0.30 Use expected value to recommend a decision.Sun TV sells TV sets. It does not sell smart TVs so customers do not come to Sun TV if they want to purchase smart TVs. Sun TV wants to start selling smart TVs and will only sell smart TVs to customers to whom they advertise. Managers use customer information (income level, previous purchase history) to decide which customers they should target. The team needs to decide how sure it must be in predicting customer interest in a smart TV. If it is too cautious, it will choose a very high cutoff probability and only market to customers who it believes are very likely to be in the market for a smart TV. This may cause them to miss out on many customers. If they are too aggressive and choose a low cutoff probability, they may identify more individuals interested in buying smart TVs but also end up wasting marketing dollars on customers who are not interested in purchasing smart TVs. To choose a cutoff probability, the team develops the confusion matrices below for two cutoff probabilities on…
- 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 Information7. 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).A manager is going to purchase new processing equipment and must decide on the number ofspare parts to order with the new equipment. The spares cost $200 each, and any unused spareswill have an expected salvage value of $50 each. The probability of usage can be described by thisdistribution:Number 0 1 2 3Probability .10 .50 .25 .15If a part fails and a spare is not available, two days will be needed to obtain a replacementand install it. The cost for idle equipment is $500 per day. What quantity of spares should beordered?a. Use the ratio method.b. Use the tabular method (see Table 13.3).
- The Valley Wine Company purchases grapes from either of two nearby grape growers each season to produce a particular red wine. It purchases enough grapes to produce 3000 bottles of the wine. Each grower supplies a certain portion of poor quality grapes, resulting in a percentage of bottles being used as fillers for cheaper table wines according to the following probability distribution. Probability of Percent Defective Defective (%) Grower A Grower B 2 .15 .30 4 .20 .30 6 .25 .20 8 .30 .10 10 .10 .10 The two growers charge a different prices for their grapes and because of differences in taste, the company charges different prices for their wine depending on which grapes they use. The annual profit from the wine produced from each grower's grapes for each percentage defective is as follows. PROFIT DEFECTIVE GROWER A GROWER B 2% $44,200 $42,600 4 40,200 40,300 6 36,200 38,000 8 32,200 35,700 10 28,200 33,400 Use decision-tree…Very Favorable Average Market Unfavorable Alternatives Market Market Build new plant $250,000 $180.000 - S200,000 Subcontract $270.000 $185,000 - $220,000 Overtime S100.000 $50,000 - $12.000 Do Nothing SO SO $0 a) Using the decision making under uncertainty with the criterion of Maximax The appropriate decision will be The value of the return under this decision is $ b) Using the decision making under uncertainty with the criterion of Maximin The appropriate decision will be The value of the return under this decision is $ c) Using the decision making under uncertainty with the criterion of Equally Likely The appropriate decision will be The value of the return under this decision is $ (enter your answer as a whole number).The medical team at Birzeit Hospital are not sure whether to buy the COVID-19 vaccine from supplier A, B, or C. The analysis of previous experience dealing with the three suppliers reveals the following vaccine quality: Percent of ineffective vaccines Probability for Supplier A Probability for Supplier B Probability for Supplier C 2 0.60 0.50 0.70 5 0.30 0.30 0.00 7 0.10 0.20 0.30 The hospital buys 25000 vaccines each year which means that the probability to get 2% ineffective vaccines is 0.60 from supplier A, 0.50 from supplier B, and 0.70 from supplier C. Develop a decision tree to show your recommended alternative (supplier).
- The following payoff table shows the profit for a decision problem with two states of nature and two decision alternatives. Decision Alternative State of Nature $1 d₁ d₂ (a) Suppose P(s₁) = 0.2 and P(5₂) = 0.8. What is the best decision using the expected value approach? The best decision is --?-- with an expected value of 12 $₂ 6 3 5 (b) Perform sensitivity analysis on the payoffs for decision alternative d₂. Assume the probabilities are as given in part (a), and find the range of payoffs under states of natures, and so that will keep the solution found in part (a) optimal. As long as the payoff for s₁ under d₁ is --?-- , then the solution found in part (a) will be optimal. then the solution found in part (a) will be optimal. As long as the payoff for s₂ under d₁ is --?-- Is the solution more sensitive to the payoff under state of nature s₁ or 5₂? O $₁ 0 5₂c. From the following decision tree, develop a payoff table and calculate: * Maximax, Minimax regret, Maximin, and EMV. ORs. 50,000 Good conditions (0.60) Poor conditions (0.40) -O Rs. 30,000 Apartment Building Good conditions (0.60) O Rs. 100,000 Office building Poor conditions (0.40) Purchase ORs -40,000 Warchouse Good conditions (0.60) Rs.30, 000 Poor conditions (0.40) O Rs. 10,000Aqua Man Company manufactures and sells a single product. Planned and actual production in its first year of operation was 100,000 units. Planned and actual costs for the year were as follows: Manufacturing Non-manufacturing Variable P600,000 P500,000 Fixed P400,000 P300,000 The company sold 85,000 units of product at a selling price of P30 per unit. Using absorption costing, the company’s operating profit was Select one: a. P1,020,000 b. P975,000 c. P900,000 d. P750,000