There is an apportunity for an investor to purchase a land. Yet, there is a zoning problem. If rezoning is approved for the land as commercial

then the investor can lease the land, and make money. If not apperoved, the investor sell the land at a loss.

Profits, in thousands of dolars$)$ are shown in the following payoff table:

Decision Approved $($App$)$ Not Approved $($NotApp$)$

Purchase $($P$)750-300$

Do not Purchase $($NP$)00$

a$)$ If the probability that the rezoning will be approve d is $0\mathrm{.}6,$ what decision is recommended?

What is the expected profit? b$)$ The investor can purchase an option to buy the land. Under the option, the investor

maintains the rights to purchase the land anytime during the next three months

while learning more about possible resistance to the rezoning proposal from area

residents. Probabilities are as follows:

Lets assume that H $=$ high resistance to rezoning P$($H$)=0\mathrm{.}57$ P$($App$|$H$)=0\mathrm{.}18$ P$($NotApp$|$H$)=0\mathrm{.}82$

L $=$ low resistance to rezoning P$($L$)=0\mathrm{.}43$ P$($App$|$L$)=0\mathrm{.}88$ P$($NotApp$|$L$)=0\mathrm{.}12$

What is the optimal decision strategy if the investor uses the option period to learn more about the resistance

from area residents before making the purchase decision?

c$)$ If the option will cost the investor an additional $$10,000,$ should the investor purchase the option? Why or why not?

What is the maximum that the investor should be willing to pay for the option?