Use PrecisionTree to solve problem 7 of the previous section.

Problem 7

Sometimes a "single-stage" decision can be broken down into a sequence of decisions, with no uncertainty resolved between these decisions. Similarly, uncertainty can sometimes be broken down into a sequence of uncertain outcomes. Here is a typical example. A company has a chance to bid on a government project. The company first decides whether to place a bid, and then if it decides to place a bid, it decides how much to bid. Once these decisions have been made, the uncertainty is resolved. First, the company observes whether there are any competing bids. Second, if there is at least one competing bid, the company observes the lowest competing bid. The lowest of all bids wins the contract. Draw a decision tree that reflects this sequence. There should be two "stages" of decision nodes, followed by two "stages" of probability nodes. Then label the tree with some reasonable monetary values and probabilities, and perform the folding back process to find the company's best strategy. Note that if the company wins the contract, its payoff is its bid amount minus its cost of completing the project minus its cost of preparing the bid, where these costs are assumed to be known.