At a decision point in a decision tree, which machine would you select when trying to maximize payoff when the anticipated benefit of selecting machine A is $45,000 with a probability of 90%; the expected benefit of selecting machine B is $80,000 with a probability of 50% and the expected benefit of selecting machine C is $60,000 with a probability of 75%? Machine A Machine B O Machine C O You would be indifferent between machines A and B
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- It costs a pharmaceutical company 75,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for the drug is unknown, with the best case being 20,000 pounds, the most likely case 17,500 pounds, and the worst case 10,000 pounds. The drug sells for 125 per pound and leftover amounts of the drug can be sold for 30 per pound. To maximize annual expected profit, how many batches of the drug should the company produce? You can assume that it will produce the batches only once, before demand for the drug is known.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.The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.
- The maximin approach to decision-making refers to: a. choosing the alternative with the minimum payoff b. choosing the alternative with the highest payoff c. maximizing the minimum expected value d. maximizing the minimum return e. minimizing the maximum returnA 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 small building contractor has recently experienced two successive years in which work opportunities exceeded the firm’s capacity. The contractor must now make a decision on capacity for next year. Estimated profits under each of the two possible states of nature are as shown in the tablebelow. Which alternative should be selected if the decision criterion is:a. Maximax?b. Maximin?c. Laplace?d. Minimax regret?NEXT YEAR’SDEMANDAlternative Low HighDo nothing $50* $60Expand 20 80Subcontract 40 70
- PT. Corona is currently trying to determine the size of the computer system which will provide optimal cost consequences when using the leasing method. The results of each decision choice and acceptance of the business situation (high and low) are summarized in the following table. Situation: Reception High $ 300,000 $ 200,000 $ 100,000 Alternative decisions Low Great leasing system Medium system leasing Small leasing system -$ 15,000 $ 20,000 $ 60,000 The director of this company wants to know which decision is best based on several approaches, namely a) approach optimistic, b) approach conservative, c) approach minimax-regret. Help the Director find the answer.The proposed Ghana Airways Airline project is being procured through a Public-Private Partnership (PPP). In the PPP procurement process, two companies (the SPVs-special purpose vehicles), ‘A’ and ‘B’ with each having 0.5% chances of selection. The risks analysis document reveals that SPV ‘A’ has 0.4 risk of performance failure, whiles SPV ‘B’ has 0.3 risk of performance failure. Using Decision Tree Analysis, as a project manager, critically assess the options and advise on the best SPV to be chosen.Chemitronix Ltd. is a microchips manufacturing company. It was found that the business is at the maturity stage, demanding some change. After rigorous research, management came up with the following decision variables Expansion: 45% chance of gaining 1,500,000; 55% chance of losing X New Product: 50% chance of gaining 900,000; 50% chance of losing 545959 What must have been the value of expansion loss if expansion and new product will result to the same expected monetary values?
- The following table is a payoff matrix associated with a farmer’s decision to purchase a pump for irrigation or to depend on the rains d) Draw up a regrets table and use it to determine which alternative will bechosen under the minimax regret decision criterion.(e) Estimate the expected value of perfect information (EVPI)Ralph Dodd, a concessionaire for the local ballpark, has developed a table of conditional values for the various alternatives (stocking decision) and states of nature (size of the crowd). LARGE AVERAGE SMALL PROBABILITY .3 .5 .2 ALTERNATIVE 1 9,000 12,000 -2,000 ALTERNATIVE 2 22,000 6,000 6,000 ALTERNATIVE 3 15,000 12,000 5,000 The probabilities associated with the states of nature are 0.30 for a large crowd, 0.50 for an average crowd, and 0.20 for a small crowd. a) The opportunity cost for choosing Alternative 2 in the presence of a large crowd is: b) The minimum expected opportunity loss is: c) The maximum amount of money that Ralph should be willing to pay for the perfect information is:Given the following conditional value table: States of Nature Very Favorable Average Unfavorable Alternatives Market Market Market Build new plant $250,000 $270,000 $180,000 $185,000 $50,000 $0 - $200,000 - $220,000 Subcontract $100,000 $0 Overtime - $12,000 Do Nothing $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).