. Question 1 Which of the following is incorrect regarding decision trees? O branches that originate from a circle node represent states of nature Oif a decision problem can be organized in a table, it can be converted to a decision tree O branches that originate from a square node are decision alternatives O calculations are usually made at event (chance) nodes O probabilities can also be assigned to the decision alternatives. Question 2 The following payoff table consists of profits ($'000) a company will earn based on their choice from alternatives d1, d2, and d3, and the resulting state of nature ($1, $2, $3). P($1) = 0.2 and P($3) = 0.6. $2 d 37 40 28 28 38 33 d3 53 47 39 a) What is the expected value of d2? Round to the nearest dollar. $ b) What is the expected value of the optimal decision? Round to the nearest dollar. $ c) What is the optimal decision based on expected values? di d2 d3 $1 $2 53. Question 3 Use the payoff table below to answer the questions that follow. Payoffs represent profits, in dollars, and the probabilities of the states of nature are given in the table. $1 $2 $3 d1 3000 2600 -1150 d2 2900 2200 -1100 d3 2800 2300 -1000 d4 3050 2000 -1050 Probability 0.3 0.3 0.4 a) What is the expected value of the optimal decision? b) What is the expected value with perfect information (EVwithPI)? c) What is the expected value of perfect information (EVPI)? $. Question 4 Use the given decision tree to answer the questions that follow. Payoffs are profits. s1 (0.68) $8,200 A -$600 $3,000 B $4,200 a) The expected value at node A, EV (A) = $ b) The expected value at node B, EV (B) = $ c) The expected value at node C, EV (C) = $The following results were obtained in a decision problem where payoffs are profits l$l: What is the expected value of the optimal decision, Maximum EMU? .- n. a. .- . Question 6 Use the given decision tree to answer the questions that follow. Payoffs are profits/losses. (0.25) -$1,500 A $2,500 (0.65) $2,500 (0.25) $2,600 B (0.1) $2,200 $3,900 a a) The expected value of alternative A, EV(A) = $ b) The expected value of alternative B, EV (B) = $ c) Which alternative is better? [Select an answer v d) EV withPI = $ e) EVPI = $. Question 7 A medical equipment manufacturer must decide whether to manufacture a new component in-house, or purchase it from an external supplier, or do neither. Their success will depend on the severity of the second wave of an impending pandemic. Experts have predicted that there is a 34% chance that the second wave will be severe and a 66% chance that it will be mild. If the second wave is severe, the company will earn $0.61 million in profits if they manufacture, and $0.2 million if they purchase. If the second wave is mild, the company will lose $163,000 if they manufacture but still earn $69,000 in profits if they purchase. a) Select the decision tree below that best represents this decision problem. b) What is the optimal expected monetary value of this decision? $ c) Based on expected values, what is the best decision for this company? O Manufacture or Purchase O Purchase O Choose severe O Do nothing O Choose mild O Manufacture. Question 8 Given the following profit payoff table: d1 160 80 330 290 -50 330 da 170 -50 390 1. Construct an opportunity loss (regret) table by completing the following table. $1 82 83 d1 d2 d3 2. Given the probabilities of the states of nature are P($1) = 0.2, P($2) = 0.3, and P(s3) = 0.5, calculate the minimum expected opportunity loss. Minimum EOL = 3. What is the best alternative based on expected opportunity loss? di d2 d3 81 $2 83 o0 0 0 0 0 4. What is the EVPI?. Question 9 Which of the following is true? O The Minimum EOL of an alternative can never be negative. O The EOL criterion selects the alternative with the largest expected opportunity loss. O The EVPI equals the largest expected opportunity loss. O The expected value of an alternative can never be negative. O The Minimum EOL approach produces the same expected value as the Maximum EMV approach.. Question 10 The hiring process at Queensway Staffing Agency is great, but far from perfect. Good candidates are sometimes rejected and bad ones sometimes hired. Since the agency earns profits from hiring good candidates, they also incur losses when they hire a candidate that is fired within 6 months or when they fail to hire (reject) a good candidate. They used relative frequency to determine the probability of hiring a good candidate and presented their payoffs (in $'000) as follows: Good Bad Hire 14.5 -4.75 Reject -2.75 0 Probability 0.28 0.72 Note: Payoffs in the given table are in thousand dollars. The expected values required below are in dollars. a) The expected monetary value of Hire is $ b) The expected monetary value of Reject is $ c) Using the expected value approach, is Queensway more likely to hire or reject a candidate? Select an answer V d) If Queensway could know if a candidate is Good or Bad with certainty, what is the expected value of that information? $. Question 11 A DECISION PAYOFF MODEL Westhumber Retail is considering the quantity of smartwatches (150, 200, or 250 units) to order and, hopefully, sell during the next holiday sale. They believe there will be low demand (100 units) for the smartwatch with 30% chance, moderate demand (150 units) with 50% chance, and high demand with (200 units) with 20% chance. Westhumber buys each smartwatch at $240 and sells them for $400 each. Smartwatches not sold over the holidays are guaranteed to be sold off during post- holiday sale at $250 each. They decided to create a payoff model for generating gross profit as follows: Payoff = (price x minimum(order, demand)) - (cost x order) + post-holiday revenue (if any) Post-holiday revenue = maximum (post-holiday price x (order - demand), 0) For example, if they order 250 units and demand is 150 units, their gross profit will be ($400 x 150) - ($240 x 250) + $250 x (250 - 150) = $25,000 Note: Post-holiday revenue can be only realized if supply is greater than demand. a) Use the given information to complete the following payoff table. PAYOFF TABLE Demand = Demand = Demand = 100 units 150 units 200 units Order 150 units Order 200 units Order 250 units $25,000 b) What is the expected value of the optimal decision