$2$

Problem $5-9($Algo$)$

$50$ points

$01$:$52$:$32$

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Hint

References

A builder has located a piece of property to buy and eventually build on$.$ The land is currently zoned for four homes per acre, but new zoning can be requested. What is built depends on approval of zoning requests and your analysis of this problem as an advisor. With the builder's input and your help, the decision process has been reduced to the following costs, alternatives, and probabilities:

Cost of land: $$3$ million.

Probability of rezoning: $0\mathrm{.}60.$

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 $1,150$ apartments that the tentative plan shows would be possible. If the shopping center is built, there is a $50$ percent chance that it can be sold to a large department store chain for $$5$ million over the construction cost, which excludes the land; and there is a $50$ percent chance that it can be sold to an insurance company for $$7$ million over the construction cost $($also excluding the land$).$ If$,$ instead of the shopping center, they decide to build the $1,150$ apartments, the proba$$ities on the profits are as follows: There is a $60$ percent chance that the apartment can be sold to a real estate investment corporation for $$4,000$ each over the construction cost; there is a $40$ percent chance that the builder can get only $$2,200$ each over the construction cost. $($Both exclude the land cost.$)$

If the land is not rezoned, the contractor will comply with the existing zoning restrictions and simply build $650$ homes, on which there are expected profits of $$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.

B$.$what is the expected value for the region apartments if the zoning cost is included but land cost is excluded.

C$.$

If the land is re$-$zoned what should the contractor decide?

Expected value mill