George Goleb is considering the purchase of two types of industrial robots. The ROB1 is a large robot capable of performing a variety of tasks, including welding and painting. The ROB1 is a smaller and slower robot, but it has all the capabilities of ROB1. The robots will be used to perform a variety of repair operations on large industrial equipment. Of course, George can always do nothing and not buy any robots.

The market for the repair operation could be either favourable or unfavourable. If the market is favourable ROB1 is expected to return $50,000 profit and ROB2 $30,000 profit. If the market is unfavourable ROB1 is expected to lead to a loss of $40,000 and ROB2 to a loss of $20,000.

1. Construct a payoff matrix showing the 3 possible alternatives and the associated profits or losses under the 2 market conditions.
2. Showing all calculations, what is the optimum action and its expected payoff if George is an optimist?
3. Showing all calculations, what is the optimum action and its expected payoff if George is a pessimist?
4. Showing all calculations, what is the optimum action and its expected payoff if George follows the Laplace criterion?
5. Showing all calculations, what is the optimum action and its expected payoff if George uses the criterion of regret?
6. If George believes that the probability of a favourable market is 0.6, showing all calculations determine the optimum action and expected return.
7. What is the expected value of perfect information?