Q$1$ Bill Holliday is not sure what he should do$.$ He can build a quadplex $($i$.$e$.,$ a building with four apartments$),$ build a duplex, gather additional information, or simply do nothing. If he gathers additional information, the results could be either favorable or unfavorable, but it would cost him $$3,000$ to gather the information. Bill believes that there is a $50-50$ chance that the information will be favorable. If the rental market is favorable, Bill will earn $$15,000$ with the quadplex or $$5,000$ with the duplex. Bill doesn't have the financial resources to do both. With an unfavorable rental market, however, Bill could lose $$20,000$ with the quadplex or $$10,000$ with the duplex. Without gathering additional information, Bill estimates that the probability of a favor$-$able rental market is $0\mathrm{.}7.$ A favorable report from the study would increase the probability of a favorable rental market to $0\mathrm{.}9.$ Furthermore, an unfavorable re$-$ port from the additional information would decrease the probability of a favorable rental market to $0\mathrm{.}4.$ Of course, Bill could forget all of these numbers and do nothing. Draw the decision tree and select the best alternative for Bill.