LaToya Jones is contemplating investing in development of a beach-front community on the Gulf of Mexico in Florida's panhandle near Pensacola. Her investment group, LTJ, would first purchase the large plot of land and then begin development.  The land area is currently zoned for residential single-family housing, but LaToya is planning to apply for re-zoning. The decision on what to build on the land will depend on whether re-zoning will be approved.  LaToya's decision on whether or not to purchase the land will depend on the following costs, options, and probabilities:

The land costs $2.5 million.  If LaToya decides to purchase the land, LTJ will submit an application for rezoning.  There is a 40% possibility that the rezoning will be approved.  If the rezoning is approved, there will be an additional cost of $1.9 million dollars for new roads, water supply, sewage, gas, and electric.

If the rezoning is approved, LaToya will need to decide whether to build a shopping center or a large apartment complex.  If the shopping center is chosen, there is a 70% chance that they will be able to sell the shopping center to a large department store chain for $5.5 million over her construction cost.  There is a 30% chance that instead, they will sell it to private equity company for $6.9 million over the construction cost. On the other hand, instead of the shopping center, they can build the large apartment complex with 1,600 units.  If the apartments are built, LaToya predicts that there is a 85% chance that the apartments can be sold to a real estate investment corporation for $3,900 each over construction cost and a 15% that they can be sold for only $2,800 each above the construction cost.

If the land is not rezoned, LaToya will comply with the existing zoning requirements and build 170 single-family homes, where they will make $9,000 profit above construction cost on each one.

LaToya faces a dilemma.  Should they buy the land?  If they buy the land and rezoning is approved, what should they do with the land?  Help LaToya by analyzing the problem.

Develop a decision tree for this problem and determine the optimal decision strategy.