Problem 1. A firm is considering two business projects. Project A will return a loss of $5 if conditions are poor, a profit of $35 if conditions are good, and a profit of $95 if conditions are excellent. Project B will return a loss of $15 if conditions are poor, a profit of $45 if conditions are good, and a profit of $135 if conditions are excellent. The probability distribution of conditions follows:
Conditions: Poor Good Excellent
Probabilities: 40% 50% 10%
(i) Calculate the expected value of each project and identify the preferred project according to this criterion.
(ii) Calculate the standard deviation of each project and identify the project that has the higher level of risk.
(iii) Calculate the coefficient of variation for each project and identify the preferred project according to this criterion.
Problem 2. A firm is considering three business projects. Project A will return a profit of $5 if conditions are poor, $10 if conditions are good, and $15 if conditions are excellent. Project B will return a profit of $12 if conditions are poor, $8 if conditions are good, and $4 if conditions are excellent. Project C will return a profit of $3 if conditions are poor, $20 if conditions are good, and $7 if conditions are excellent.
(i) Use the maximum criterion to determine the preferred project. Show how you arrived at your solution.
(ii) Calculate the regret matrix.
(iii) Use the minimax regret criterion to determine the preferred project. Show how you arrived at your solution.