Mack is trying to invest in any of the following business ventures: Flying Schools, Manufacturing, Education and Security Systems which can occur under three states of nature namely low economy performance, medium economy performance and high economy performance. The probability of a low economy performance occurring is four times that of the medium economic performance. The probability of a high economy performance occurring is 0.4 investing in Flying Schools yields P15 million under low economic performance, P10 million under medium economic performance and a loss of P2 million under high economic performance. Choosing manufacturing results in P20 million, P6 million and P17 million under low, medium and high economic performance respectively. If he chooses Education, he expects to yield P10 million, P35 million and P 8 million in low, medium and high economic performance respectively. Security Systems can result in payoffs of P4 million, -P2 million and P40 million under low, medium and high economic performance respectively.

a. Construct the payoff table for Mack.

b. Represent the information using a decision tree diagram showing all the labels.

c. Determine the decision alternatives if:

i. Mack is optimistic. (1 mark)

ii. Mack is pessimistic. (1 mark)

iii. Mack uses probabilities.

iv. Mack wants to always keep regret at a minimum. (4 marks)

d. If Mack gets some accurate information that will help him yield maximum payoff, calculate how much he would be prepared to pay for that information?