A builder has located a piece of property that she would like to buy and eventually build on. The land is currently zoned for four homes per acre, but she is planning to request new zoning. What she builds depends on the approval of zoning requests and your analysis of this problem to advise her. With her input and your help, the decision process has been reduced to the following costs, alternatives and probabilities:

Cost of land: $2 million

Probability of rezoning: 0.60

If the land is rezoned, there will be additional costs for new roads, lighting and so on, of $1 million

If the land is rezoned, the contractor must decide whether to build a shopping center or 1,500 apartments that the tentative plan shows would be possible. If she builds a shopping center, there is 0.70 chance that she can sell the shopping center to large department store for $4 million over her construction cost, which excludes the cost of land; there is 0.30 chance that she can sell it to an insurance company for $5 million over her construction cost (also excluding the land cost). If, instead of the shopping center she decides to build the 1,500 apartments, she places probabilities as follows: There is 0.60 chance that she can sell the apartments to a real estate investment corporation for $3,000 over her construction cost; there is 0.40 chance that she can get only $2,000 over her construction cost. (Both exclude the land cost.)

If the land is not rezoned, she will comply with the existing zoning restrictions and simply build 600 homes, on which she expects to make $4,000 over the construction cost on each one (again, excluding the cost of land).

Draw a decision tree of the problem and determine the best action and the expected net profit. ( You may draw the decision tree by hand and scan and add to you submission, if you so wish.).