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- 2. A toy manufacturer has three different mechanisms that can be installed in a doll that it sells. The different mechanisms have three different setup costs (overheads) and variable costs and, therefore, the profit from the dolls is dependent on the volume of sales. The anticipated payoffs are as follows. Light Demand 0.25 $325,000 $300,000 -$400,000 Heavy Demand 0.3 Probability Wind-up action Pneumatic action Electrical action Moderate Demand 0.45 $190,000 $420,000 S170,000 $400,000 $800,000 $240,000 a. What is the EMV of each decision alternative? b. Which action should be selected? c. What is the expected value with perfect information? d. What is the expected value of perfect information? e. What is the expected opportunity loss?Problem 4-11 (Algorithmic) Following is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project. Amounts are in millions of dollars. State of Nature Decision Alternative Strong Demand S₁ Weak Demand S₂ Small complex, di 6 Medium complex, dz Large complex, d3 8 14 20 3 -8 Suppose PDC is optimistic about the potential for the luxury high-rise condominium complex and that this optimism leads to an initial subjective probability assessment of 0.78 that demand will be strong (S₁) and a corresponding probability of 0.22 that demand will be weak (S₂). Assume the decision alternative to build the large condominium complex was found to be optimal using the expected value approach. Also, a sensitivity analysis was conducted for the payoffs associated with this decision alternative. It was found that the large complex remained optimal as long as the payoff for the strong demand was greater than or equal to $17.1 million and as long as the payoff for the weak demand…A local toy manufacturer has three different mechanisms that can be installed in a doll that it sells. The different mechanisms have three different setup costs (overheads) and variable costs and, therefore, the profit from the dolls is dependent on the volume of sales. The anticipated payoffs are as follows: Light Demand Moderate Demand Heavy Demand Probability 0.25 0.45 0.3 Wind-up action $325,000 $190,000 $170,000 Pneumatic action $300,000 $420,000 $400,000 Electrical action -$400,000 $240,000 $800,000 What is the ultimate objective in the use of decision trees to product design? How is this objective accomplished? Draw the decision tree. What is the EMV of each decision alternative? Which action should be selected?
- 20. The Video Game Supply Company (VGS) is deciding whether to set next year's production at 2000, 2500, or 3000 games. Demand could be low, medium, or high. Using historical data, VGS estimates the probabilities as: 0.4 for low demand, 0.3 for medium demand, and 0.3 for high demand. The following profit payoff table (in $100s) has been developed. Demand Production Target Low Medium High 2000 games 2500 games 3000 games 1000 1200 1400 800 1500 1300 600 1700 1400 (a) [1] What is the maximax decision alternative? (b) [1] What is the maximin decision alternative? (c) [2] Determine the expected value of each alternative and indicate what should be the production target for next year based on expected value. (d) [1] Determine the expected value with perfect information about the states of nature. (e) [1] Determine the expected value of perfect information.Problem 13-11 (Algorithmic) Following is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project. Amounts are in millions of dollars. State of Nature Decision Alternative Strong Demand S1 Weak Demand S2 Small complex, d1 8 6 Medium complex, d2 14 5 Large complex, d3 19 -8 Suppose PDC is optimistic about the potential for the luxury high-rise condominium complex and that this optimism leads to an initial subjective probability assessment of 0.8 that demand will be strong (S1) and a corresponding probability of 0.2 that demand will be weak (S2). Assume the decision alternative to build the large condominium complex was found to be optimal using the expected value approach. Also, a sensitivity analysis was conducted for the payoffs associated with this decision alternative. It was found that the large complex remained optimal as long as the payoff for the strong demand was greater than or equal to $17.25 million and as long as the payoff…A decision maker has prepared the following payoff table. States of Nature Alternative High Low Buy 75 -10 Rent 70 30 Lease 50 35 Prior Probability 0.5 0.5 Using Baye's Decision Rule, what is the best decision and the expected payoff? (Round your answer to 1 decimal place.) Best decision Рayof
- #6) A group of medical professionals is considering constructing a private clinic. If a patient demand for the clinic is high, the physicians could realize a net profit of $120,000. If the demand is low, they could lose $55,000. Of course, they do not have to proceed at all, in which case there is no cost. In the absence of any market data, the best the physicians can guess is that there is a 50-50 chance the demand would be high. a) Create a decision tree. b) What should the medical professionals do? What is the payoff? c) The physicians have been approached by a market research firm that offers to perform a study of the market at a fee of $5,000. The market researchers claim that their experience enables them to use Bayes’ theorem to make the following statements of probability: -probability of high demand given a positive survey result = 0.82 -probability of low demand given a positive survey result = 0.18 -probability of high demand given a negative survey result = 0.11…A payoff table is given as: S1 S2 S3 D1 250 750 500 D2 300 -250 1200 D3 500 500 600 (a) What choice should be made by the optimistic decision maker? (b) What choice should be made by the conservative decision maker? (c) What decision should be made under minimal regret? (d) If the probabilities of d1, d2, and d3 are .2, .5, and .3, respectively, then what choice should be made under expected value?Following is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project. Amounts are in millions of dollars. State of Nature Decision Alternative Strong Demand S1 Weak Demand S2 Small complex, d1 8 7 Medium complex, d2 14 5 Large complex, d3 20 -9 Suppose PDC is optimistic about the potential for the luxury high-rise condominium complex and that this optimism leads to an initial subjective probability assessment of 0.8 that demand will be strong (S1) and a corresponding probability of 0.2 that demand will be weak (S2). Assume the decision alternative to build the large condominium complex was found to be optimal using the expected value approach. Also, a sensitivity analysis was conducted for the payoffs associated with this decision alternative. It was found that the large complex remained optimal as long as the payoff for the strong demand was greater than or equal to $17.5 million and as long as the payoff for…
- The following payoff table provides profits based on various possible decision alternatives adn various levels of demand at Robert Klassan's print shop: decision low high alt 1 $10,000 $36,000 alt 2 $6,000 $38,000 alt 3 -$2500 $52,000 The probability of low demand is 0.40 whereas the probability of high demand is 0.60. a) The alternative that provides Robert the greatest expected monetary value is _________ The EMV for this decision is $_______ b) The expected value with perfect information (EVwPI)= $______ c) The expected value of perfect information (EVPI) for Robert= $________Payoff Table Decision Alternatives Demand Low Medium High Small, d1 400 500 600 Medium, d2 100 600 800 Large, d3 -300 400 1200 1). If nothing is known about the demand probabilities, what are the recommended decision using the Maximax (optimistic), Maximin (pessimistic) and Equally Likely? 2). If P(low) = 0.20, P(medium) = 0.35, and P(high) = 0.45. What is the recommended decision using the expected monetary value approach? 3). What is the expected value of perfect information (EVPI)?3. A toy manufacturer makes stuffed kittens and puppies which have relatively lifelike motions. There are three different mechanisms that can be installed in these "pets." These toys will sell for the same price regardless of the mechanism installed, but each mechanism has its own variable cost and setup cost. Profit, therefore, is dependent upon the choice of mechanism and upon the level of demand. The manufacturer has in hand a forecast of demand that suggests a 0.2 probability of light demand, a 0.45 probability of moderate demand, and a probability of 0.35 of heavy demand. Payoffs for each mechanism-demand combination appear in the table below. Wind-up action Pneumatic action Electronic action Demand Light Moderate $250,000 $90,000 -$100,000 400,000 440,000 400,000 Heavy 650,000 740,000 780,000 Construct the appropriate decision tree to analyze this problem. Use standard symbols for the tree. Analyze the tree to select the optimal decision for the manufacturer.
