A contractor has found that her cost for a certain construction job is subject to random variation. She believes its actual value follows a continuous uniform distribution between $9000 and $11000 with a mean of $10,000. The cost to prepare her bid is $500. She is competing in a sealed bid competition with four other contractors. She believes that the bids submitted by the other contractors will vary uniformly between her mean cost and 3 times her mean cost and that their bids are independent of each other. She will win the competition if her bid is smaller than the bids of all four competitors. If she wins, her profit will be the difference between her bid and her cost minus the proposal preparation cost. If she loses her proposal preparation cost is lost and her profit is -$500.
Simulate 1000 bids in which her bid amount is $14,000 and determine the distribution of her profit. Determine the probability that she wins the competition and the probability that she loses money. Compare these results for bid amounts of $13000 and $15000