Ch. 3 Assigned HW 1. Your neighbor Mr. Rodgers has run a business that makes and sells industrial refrigerators. To deal with more intense competition he is thinking to buy a new type of refrigerator, either a TagmayPlus, a MarkerHigh, or a Elec Special. His marketing group has determined that either a favorable market or an unfavorable market are the only reasonable outcomes. If he purchases a TagmayPlus and the market is favorable he'll realize a profit of $400,000, but lose $250,000 if the market is unfavorable. Purchasing a Marker High will generate payoffs of $350,000 or -S150,000, whether the market is favorable or unfavorable, respectively. However, if he buys a ElecSpecial he stands to gain a profit of 85,000 but suffer a loss of $27,000 depending on the market. (a) He is generally an optimistic decision maker, so what decision criterion should he use, and what alternative is best with this criterion? (b) His brother, however, is a finance person who has a pessimistic attitude about the business of industrial refrigerators. What decision criterion should be use and what alternative will he select? (c) A recent issue of The American Consumer forecasts a favorable market has a chance of occurrence of 40%, while the chance of an unfavorable market is What decision criterion now should be used and what is the resulting optimal solution? 2. Suppose you're considering investing some money in either the stock market, bonds, or CDs. Here is the payoff table extrapolated for the next two years that you've constructed from the website, The American Investment Trade Journal. State of Nature Decision Rising Holding Steady Declining Alternative Economy Economy Economy Stock market $48.000 30.000 -20,000 Bonds 26,000 22,000 10.000 21.000 21,000 21.000 CDs (a) Wiat decision of the given die should you make were you an optimist? (b) If you are an undying possimist by nature, what alternative would you choose? (e) Suppose. however, you're indifferent to the states of nature and feel they are equally likely to occur. What douision would you make then 3. (a) Consider the previous problem. Although not always a daily pessimist, you might apply the model Minimax Regret. if you want to minimize your losses expressed a regrets. What decision would you now make when this model is applied? (b) Altematively, if you awoke today and felt two parts optimize to three parts pessimistie. wlidt decision wuld you make? You must first daterie de coefficient of realism, 4. Janet Smith manages the PQR Drilling Products, a company that manufactures certain valves for oil field equipment. Due to rising activity in the oil fields the last few weeks, demand for these valves has increased steadily over the last few weeks, encouraging Ms. Smith to open a new production facility, either in Oklahoma, Louisiana, or Texas. The exact location in either state is not yet clear, so Ms. Smith and advisees have labeled the locations as A, B, and C, respectively. It is expected that demand will be low, medium, or high with estimated probabilities 20%, 30%, and 50%. Moreover, the monthly payout in thousands for the constructed Oklahoma site (A) is $90, $115, and $155 according to demand being low, medium, or high. The corresponding payouts if the chosen site is Louisiana (B) are $95, $105, and $145 for the same demand sequence. It also has been determined that the consecutive payouts for demand at the Texas location (C) are $115, $125, and $135. (a) Which location should be selected based on the minimax regret criterion? (b) Which location should be selected for maximizing the expected payouts? (c) Which location will minimize the expected opportunity loss? (d) How much is a perfect forecast of demand worth? (e) What is the most Ms. Smith would be willing to pay for a newsletter that claims to be very good at predicting the demand for oil in the South
