Q1. Today's Electronics specializes in manufacturing modern electronic components. It also builds the equipment that produces the components. Phyllis Weinberger, who is responsible for advising the president of Today's Electronics on electronic manufacturing equipment, has developed the following table concerning a proposed facility: PROFIT ($) STRONG Market FAIR market POOR MARKET Large facility 550,000 110,000 –310,000 Medium-sized facility 300,000 129,000 –100,000 Small facility 200,000 100,000 –32,000 No facility 0 0 0 (a) Develop an opportunity loss table. (b) What is the minimax regret decision? Q2. Peter Martin is going to help his brother who wants to open a food store. Peter initially believes that there is a 50–50 chance that his brother's food store would be a success. Peter is considering doing a market research study. Based on historical data, there is a 0.8 probability that the marketing research will be favorable given a successful food store. Moreover, there is a 0.7 probability that the marketing research will be unfavorable given an unsuccessful food store. (a) If the marketing research is favorable, what is Peter's revised probability of a successful food store for his brother? (b) If the marketing research is unfavorable, what is Peter's revised probability of a successful food store for his brother? (c) If the initial probability of a successful food store is 0.60 (instead of 0.50), find the probabilities in parts a and b. Q3. A financial advisor has recommended two possible mutual funds for investment: Fund A and Fund B. The return that will be achieved by each of these depends on whether the economy is good, fair, or poor. A payoff table has been constructed to illustrate this situation STATE OF NATURE GOOD FAIR POOR INVESTMENT ECONOMY ECONOMY ECONOMY Fund A $10,000 $2,000 - $5,000 Fund B $6,000 $4,000 0 Probability 0.2 0.3 0.5 (a) Draw the decision tree to represent this situation. (b) Perform the necessary calculations to determine which of the two mutual funds is better. Which one should you choose to maximize the expected value? (c) Suppose there is question about the return of Fund A in a good economy. It could be higher or lower than $10,000. What value for this would cause a person to be indifferent between Fund A and Fund B (i.e., the EMVs would be the same)? Q4. Even though independent gasoline stations have been having a difficult time, Susan Solomon has been thinking about starting her own independent gasoline station. Susan's problem is to decide how large her station should be. The annual returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline. After a careful analysis, Susan developed the following table: GOOD FAIR POOR SIZE OF MARKET MARKET MARKET FIRST STATION ($) ($) ($) ------------------------------------------------------------------------- Small 50,000 20,000 –10,000 Medium 80,000 30,000 –20,000 Large 100,000 30,000 –40,000 Very large 300,000 25,000 –160,000 For example, if Susan constructs a small station and the market is good, she will realize a profit of $50,000. (a) Develop a decision table for this decision. (b) What is the maximax decision? (c) What is the maximin decision? (d) What is the equally likely decision? (e) What is the criterion of realism decision? Use an  value of 0.8. (f) Develop an opportunity loss table. (g) What is the minimax regret decision? Q5. The total expenses of a hospital are related to many factors. Two of these factors are the number of beds in the hospital and the number of admissions. Data were collected on 14 hospitals, as shown in the table below: NUMBER ADMISSIONS TOTAL EXPENSES HOSPITAL OF BEDs (100s) (MILLIONS) 1 215 77 57 2 336 160 127 3 520 230 157 4 135 43 24 5 35 9 14 6 210 155 93 7 140 53 45 8 90 6 6 9 410 159 99 10 50 18 12 11 65 16 11 12 42 29 15 13 110 28 21 14 305 98 63 Find the best regression model to predict the total expenses of a hospital. Discuss the accuracy of this model. Should both variables be included in the model? Why or why not? Q6. A sample of 20 automobiles was taken, and the miles per gallon (MPG), horsepower, and total weight were recorded. Develop a linear regression model to predict MPG, using horsepower as the only independent variable. Develop another model with weight as the independent variable. Which of these two models is better? Explain. MPG HORSEPOWER WEIGHT 44 67 1,844 44 50 1,998 40 62 1,752 37 69 1,980 37 66 1,797 34 63 2,199 35 90 2,404 32 99 2,611 30 &nbs