Traffic has gotten so congested that there is planning underway for a new river crossing. Three proposals have been put forward: One is to build a bridge. Another is to construct a tunnel under the river. The third is to develop a ferry service. Estimates are that there is a 60% probability that traffic levels will remain the same, a 10% chance that traffic will get lighter, and a 30 % chance that traffic will get heavier. The bridge will cost $80 million initially; but if traffic gets heavier, it will need a $20 million upgrade. The tunnel will cost $60 million initially. If traffic gets heavier it can be expanded for an extra $50 million. The ferry service would cost $30 million initially. If traffic gets heavier, it would have to be supplemented by either a bridge or a tunnel. A bridge would then cost $200 million; a tunnel would then cost $300 million. Draw a decision tree for this planning problem. Solve your tree to minimize the cost of a new river crossing. Show detailed calculations for every node in your tree. What is your recommendation best thing to do and why?

Traffic has gotten so congested that there is planning underway for a new river crossing. Three proposals have been put forward: One is to build a bridge. Another is to construct a tunnel under the river. The third is to develop a ferry service. Estimates are that there is a 60% probability that traffic levels will remain the same, a 10% chance that traffic will get lighter, and a 30 % chance that traffic will get heavier. The bridge will cost $80 million initially; but if traffic gets heavier, it will need a $20 million upgrade. The tunnel will cost $60 million initially. If traffic gets heavier it can be expanded for an extra $50 million. The ferry service would cost $30 million initially. If traffic gets heavier, it would have to be supplemented by either a bridge or a tunnel. A bridge would then cost $200 million; a tunnel would then cost $300 million. a. Draw a decision tree for this planning problem. b. Solve your tree to minimize the cost of a new river crossing. Show detailed calculations for every node in your tree. c. What is your recommendation best thing to do and why