Problem $4-9($Algo$)$

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 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: $$4$ million.

Probability of rezoning: $0\mathrm{.}50.$

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 $1,100$ apartments that the tentative plan shows would be possible. If she builds a shopping center, there is a $30$ percent chance that she can sell the shopping center to a large department store chain for $$6$ million over her construction cost, which excludes the land; and there is a $70$ percent chance that she can sell it to an insurance company for $$6$ milion over her construction cost $($also excluding the land$).$ If$,$ instead of the shopping center, she decides to build the $1,100$ apartments, she places probabilities on the profits as follows: There is a $50$ percent chance that she can sell the apartments to a real estate investment corporation for $$1,500$ each over her construction cost, there is a $50$ percent chance that she can get $$2,100$ each 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 bulld $450$ homes, on which she expects to make $$3,800$ over the construction cost on each one $($excluding the cost of land$).$

a$.$ What is the expected value for the rezoned shopping center, if the rezoning cost is included $($but land cost is excluded$)?$ Note: Do not round your intermediate calculations. Enter your answers in millions rounded to $2$ decimal places. Negative amounts should be indicated by a minus sign.

Expected value

million

b$.$ What is the expected value for the rezoned apartments, if the rezoning cost is included $($but land cost is excluded$)?$

Note: Do not round your intermediate calculations. Enter your answers in millions rounded to $2$ decimal places. Negative amounts should be indicated by a minus sign.

Expected value

million

c$.$ If the land is rezoned, what should the contractor decide?

Build shopping center

Build apartments

d$.$ What is the expected revenue, if the land is not rezoned $($excluding the land cost$)?$

Note: Do not round your intermediate calculations. Enter your answers in millions rounded to $2$ decimal places. Negative amounts should be indicated by a minus sign.

Expected revenue

million

e$.$ What is the expected net profit of entire project, including all applicable costs?

Note: Do not round your intermediate calculations. Enter your answers in millions rounded to $2$ decimal places. Negative amounts should be indicated by a minus sign.

Expected net profit

million