10. (25pts) Your company is proposing fo expand the manufacturing capacity for a group of materials for an aerospace company, but will not have a decision from the aerospace company in two years. You estimate the possible future states and their probabilities as follows: Receive full contract (N1, with probability p1=0.5); receive partial contract (N2. p2=0.4); no contract (N3,p3=0.1). You must make a choice now among the three options: ji) build a new line, which will bring in profit of $50 million if full contrsct is awarded, $25 million if partial contract is awarded, but will cost a loss of 30 million if loss of contract eccurs ii) modify existing line, which will bring in profit of $30 million if full contract is awarded, $15 million for partial contract, and a loss of 15 million if no contract occurs; iii) do nothing, which will cost a loss of potential profit of $30 million in the case of full contract, and a loss of 10 million for partial contract, and no loss at all if no contract is awarded. i) Set up the payoff table ( 5pts) ii) Show which alternative maximize expected value ( 5pts ) iii) If you do not know the probabilities of getting the contract, what would be your decision based on uncertainty using (a) maximax ( 3 pts); (b) maximin (3 pts): (c) equal likely ( 3 pts) and (d) minimax regret assumptions ( 6 pts)