A real estate developer must decide on a plan for developing a certain piece of property. After careful consideration, the developer has two acceptable alternatives: residential proposal or commercial proposal. The main factor or state of nature that will influence the profitability of the development is whether or not a shopping center is built close by and the size of the shopping center. There is a $20\%$ chance of no center being built, a $50\%$ chance of a medium shopping center built, and a $30\%$ chance of a large shopping center.

If the developer selects the residential proposal and no center is built, he has a further set of options: do nothing $$400,000$ payoff; build a small shopping center himself $$700,000$ payoff, or put in a park resulting in $$800,000$ payoff. Should a medium shopping center be built nearby, his payoff for residential would be If $$1,600,000$ and large shopping center results in a $$1,200,000$ payoff.

If the developer selects the commercial proposal and no center is built, he also has the set of options: do nothing but payoff would be $$-50,000$; build a small shopping center himself for $$1,400,000$ payoff, or put in a park resulting in $$1,000,000$ payoff. Should a medium shopping center be built nearby, his payoff

$1$

for commercial would be $$400,000$ and large shopping center results in a $$1,500,000$ payoff.

a$)$ Draw a decision tree for this problem.

b$)$ Determine the EMV for the problem and identify the best decision.

Focus