Gamma Construction Company has been asked to bid on the construction of 20 lighted tennis courts for State University. Each court will cost $20,000 in construction costs, and, in addition, there will be a fixed expense of $10,000 to cover the preparation and submittal of the bid. Gamma is considering five different bid levels. Each level involves a different profit margin, calculated as a percentage above total construction cost (TCC). Fixed expenses are excluded from these calculations, but they are relevant for profitability. Based on previous experience, Gamma's management is able to estimate the probability that it will win the bid at each level being considered. The bids and the probabilities are summarized in the table below: Bid Number 1 2 Amount of Bid TCC+5% TCC+10% TCC+15% TCC+20% TCC+25% Probability of winning 0.80 0.70 0.50 0.30 3 4 5 0.20 a. Model this decision problem as a decision tree. Use as payoff the profit associated with each possible outcome. (15 points) b. Use Baye's rule to determine the optimal bid for Gamma. (15 points) c. Consider the probability of winning the optimal bid. If this probability were allowed to vary, while the other parameters were kept unchanged, what values could it take without altering the optimal solution? (BONUS 15 points)