(120 marks) Consider the following modified one-period RC model. Robinson Cru- soe (RC) is the only inhabitant of a desert island. Fortunately, the island has two separate stocks of both coconut trees and lemon trees, and Robinson Cru- soe likes to eat both coconuts and lemons. Let c be the quantity of coconuts and that he eats and I be the quantity of lemons that he eats. RC's preferences over coconuts and lemons are given by the utility function U - u(c, l), where u(.) is strictly increasing, strictly quasi-concave and twice differentiable. To get the coconuts, RC must climb the coconut trees and pull the coconuts off with his hands. The amount of coconuts y he can pick through this method is given by the production function yc - Z' f ( n' ) (3)where n is the amount of time RC spends picking coconuts, f (.) is a constant returns to scale production function with properties f, > 0, fin 0, fr