Really need help on linear programming (statistics)

Question

A television network is attempting to decide during the summer which of the following three football games to televise on the Saturday following Thanksgiving Day: Alabama versus Auburn, Georgia versus Georgia Tech, or Army versus Navy. The estimated viewer ratings for the games depend on the win–loss records of the six teams, as shown in the following payoff table:

                                                           Number of Viewers (1,000,000s)
                                                                      One Team Has
                                   Both Teams                  Winning Record; One                             Both Teams
                                  Have Winning                 Team Has Losing                                   Have Losing
Game                            Records                          Record                                               Records
Alabama vs. Auburn         10.8                                7.5                                                       4.6
Georgia vs. Georgia Tech  9.5                                 8.8                                                       4.8
Army vs. Navy                  9.6                                 8.1                                                       5.1

Determine the best game to televise and the payoff associated with it by using the following decision criteria.

a. Maximax
b. Maximin
c. Equal likelihood
d. Minimax regret

 

 

 

PART 2

 

the probabilities are given by P(both teams have winning records) = 0.4, P(one team has winning record; one team has losing record) = 0.4, and P(both teams have losing records) = 0.2.

a. Compute the expected value for each decision and select the best one.
b. Compute the expected regret value for each decision and select the best one.
c. Calculate and interpret the expected value of perfect information.

Answer 1

Here’s a short summary of the solution:

Part 1: Decision Criteria

1. Maximax (Optimistic Approach):
2. Best Game: Alabama vs. Auburn (10.8 million viewers)
3. Maximin (Pessimistic Approach):
4. Best Game: Army vs. Navy (5.1 million viewers)
5. Equal Likelihood:
6. Best Game: Georgia vs. Georgia Tech (Average: 7.7 million viewers)
7. Minimax Regret:
8. Best Game: Army vs. Navy (Regret: 1.2 million viewers)

Part 2: With Probabilities

Given probabilities:

1. P(Both teams winning) = 0.4
2. P(One team winning) = 0.4
3. P(Both teams losing) = 0.2
4. Expected Value (EV):
5. Best Game: Georgia vs. Georgia Tech (EV: 8.28 million viewers)
6. Expected Regret:
7. Best Game: Georgia vs. Georgia Tech (Regret: 0.58)
8. Expected Value of Perfect Information (EVPI):
9. EVPI: 0.58 million viewers (Additional viewers with perfect info)