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 win the bid at each level being considered. The bids and the probabilities are summarized in the following table:

 

Bid Number	Amount of Bid	Probability of Winning
1	TCC+5%	0.80
2	TCC+10%	0.70
3	TCC+15%	0.50
4	TCC+20%	0.30
5	TCC+25%	0.20

 

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

. What is the expected profit associated with the optimal bid in part (a)?