2) A real estate investor has the opportunity to purchase land currently zoned residential. Ifthe courty board approves a request to rezone the property as commercial within the next year, the investor will be able to lease the land to a large discount firm that wants to open a new store on the property. However, if the zoning change is not approved, the investor will have to sell the property at a loss. Profits (in thousands of dollars) are shown in the following payofftable: Decision altematives Rezoring approved States of Nature Rezoring not approved S2 S1 + Purchase, d1 Do not purchase, d2 260 0 -70 0 + a. Ifthe probability that the rezoring will be approvedis 0.6, what decision is recommended? What is the expected profit? (7 marks) 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 leaming more about possible resistance to the rezoning proposal from area residents. Probabilities are as follows: Let H_High resistance to rezoning L_Low resistance to rezoring P(H)= 0.65 P(S1 H)-0.25 P(S2H)= 0.75 P (L) = 0.35 P(S1L)= 0.85 P(S2L) = 0.15 Whatis the optimal decision strategy if the investor uses the option period to leam more about the resistance from area residents before making the purchase decision? (7 marks) C. If the option will cost the investor an additional $6,000, should the investor purchase the option? Why or why not? Whatis the maximum that the investor should be willing to pay forthe option? (4 marks)