House I (occupied by Amit) and House 2 (occupied by Divya) are located next to each other. Amit's family is expanding and so he wants to add two more floors to his house. He is willing to pay up to Rs. 10 lakhs for construction of the first additional floor, but only Rs. 7 lakhs for the second additional floor. He is very happy to learn that the builder would charge only Rs. 5 lakhs for construction of each floor. However, there is another issue: Divya claims that one additional floor would partially obstruct her view of the beach, and a second additional floor would do so completely. She values an unobstructed view of the beach at Rs. 12 lakhs and a partially obstructed view at Rs. 8 lakhs. (Her value for a completely obstructed view is 0.) (a) (4 marks) To maximize the sum of Amit and Divya's payoffs, how many additional floors should be constructed (0, 1, or 2)? (b) (4 marks) Suppose that Divya offers Amit some money to abandon his plans to construct one or both floors (she may make a different offer for each floor). Amit must find the offer acceptable, or else he can reject it. How many additional floors will be constructed after this negotiation (0, 1, or 2)? (c) (2 marks) Now suppose that no negotiation takes place but Amit decides to con- struct one floor (and abandon his plans to construct a second one). Just before he gets the process of construction started, Divya finds out that she can actually sue Amit to prevent him from undertaking any construction. However, for that, she would have to pay her lawyer Rs. 3 lakhs. Amit hears of this and suggests that instead of taking the legal route, the two of them can come to a settlement wherein Amit pays Divya some amount of money S and in return, she allows Amit to add one floor. What is the range of values of S for which such a plan would be agreeable to both of them