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# Decision Analysis: Gamma Construction Company

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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 this calculation, but they are relevant for profitability. Based on previous experience, Gamma's management is able to estimate the probability that it will wine the bid at each level being considered. The bids and the probabilities are summarized in the table below.

Bid Amount Probability
Number of Bid of Winning
1 TCC + 5% 0.8
2 TCC + 10% 0.7
3 TCC + 15% 0.5
4 TCC + 20% 0.3
5 TCC + 25% 0.2

Gamma's objective is to select the bid that maximizes its expected profit.

a. What is the optimal bid for Gamma to make?
b. What is the expected profit associated with the optimal bid in part (a)?
c. What is the risk profile for the optimal bid in part (a)?
d. Consider the probability of winning the optimal bid. If this parameter were allowed to vary, while all other parameters were kept unchanged, what values could it take without altering the optimal selection?

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