1. An entrepreneur is considering printing T-shirts for a football game. He could print either 10 000, 15 000 or 20 000. Demand could either be high, medium or low. For 10 000, profits would be K12 000 for high demand, K10 000 for medium and K 9 600 for low demand respectively. For 15 000, profit would be K20 000, K18 000 and K6 000 for the different states and for 20 000, profit would be K30 000, K 16 000 and K4 000 for high, medium and low demand, respectively. With the demand for T-shirts having probabilities of high, medium and low being 40%, 35% and 25%, use EMV, EOL and EVPI to determine how many T-shirts should be printed. 2. An investment manager has a dilemma of how to invest K10 000 000. He could either invest in stocks, bonds, certificates of deposit (CD) or a mixture of the three. The economy could be stagnant 25%, slow growth 45% and rapid growth 30%. For the stagnant economy -K500 000,-K100 000, K300 000 and K200 000 would be the payoffs for the different investments For the slow growth economy K700 000, K600 000, K500 000 and K650 000 would be the payoffs for the different investments For the rapid growth economy K2200 000, K900 000, K750 000 and K1300 000 would be the payoffs for the different investments. Compute the expected monetary value (EMV). 3. A landlord can either lease for one or two years or sell offices outrightly for K 100 Million with payoffs as follows: -100 Lease Sell 50 100 100 150 100 The probability of rejecting is 30%, leasing for one year is 50% and for two years 20%. What is the optimal decision strategy if perfect information were available? What is the expected value of perfect information? 4. A decision maker is looking to minimising costs through three alternative decisions A1, A2 and A3 under two states of nature events Sl and S2 with S3 having a probability of 30%. For Al payoffs for SI K100 million and S2 K540 million For A2 payoff for SI K150 million and S2-K 50 million For A3 payoff for S1 K350 million and S2 K320 million a. Find EMV and recommend the course of action b. Find the EMV under certainty c. Use the EVC to find the EVPI d. Determine the opportunity loss table e. Find the course of action that minimises EOL f. Compare the minimum EOL with the EVPI. 5. Profits for a skiing resort depends on how much snow falls in winter. The probability distribution of snowfall and resulting profitability is as follows: More than 40 inches K120 000 40% 20 to 40 inches K 40 000 20% Less than 20 inches -K40 000 40% The owner receives an offer from a hotel chain to lease the resort at a guaranteed profit of K45 000 for the season. He is also considering leasing snow making equipment which would allow the resort to operate full-time regardless of the amount of natural snow fall which would ensure profit of K120 000 minus the cost of leasing and operating the snow equipment. The leasing cost is K12 000 per season regardless of usage. Operating cost will be K10 000 for natural snowfall of more than 40 inches, KS0 000 for between 20 and 40 inches and K90 000 if it is less than 20 inches Construct a decision tree and advise on the optimal decision to be taken. 6. A would-be investor with K100 000 000 is considering investing either in the share market or the capital market in which he could earn a fixed rate of 12%. If the share market is good (with a probability of 60%), he can earn K50 000 000 on his capital without taking dividends into account but if bad or unfavourable (with a probability of 40%), he could lose K20 000 000 of his capital Use a decision tree to advise the investor. 7. A decision tree has action al with outcomes sl, s2 and s3 with payoffs K8000, K 10000 and K1000 Decision a2 with outcomes sl, s2 and s3 with payoffs K3000, K6000 and -K2000 Decision a3 with outcomes sl, s2 and s3 with outcomes K10 000,-K900 and K50 Find the actions that would be prescribed by the maximax, and maximin criterion. Explain why the action prescribed by the Maximin criterion here is potentially unreasonable from a practical viewpoint. 8. You are required to choose from two actions: Al: deposit K1 000 000 in the bank for 1 year at 7% interest A2: invest K 1 000 000 for 1 year with 50% probability of having K2 500 000 at the end of the year, and 50% probability of losing all the K 1 000 000. Which would you choose and why? 9. Branch size Sate of nature Market share during fifth year of operation S1: 0%