please do by hand

3. A home construction company has three options for the size of a new development. They must decide whether to build 50, 100 or 150 homes. Their profit depends on the eventual demand for houses. For the purposes of analysis, they consider three possible future markets in three years when the homes are available. The demand could be Low (50 homes), Moderate (100) or High (150). They estimate their potential profit in the following table: Payoff Matrix State (Demand) Low (50 Moderate (100) High (150) Alternatives: Number of homes to build 50 100 150 $400,000 $100,000 -$200,000 $400,000 $800,000 $500,000 $400,000 $800,000 $1,200,000 Suppose that they have no information about the probabilities of the demand (complete ignorance). What is the optimal decision using the rules: Maximax, Maximin, Laplace and Minimax Regret? (6 marks) Page 3 of seven pages