Robinson Crusoe lives alone on a desert island. He works 9 hours per day gathering coconuts and hunting sh. His production functions for the two goods are: C = 2 LC and F = LR\" where C and F are the quantities of coconuts and sh produced (and consumed) per day and Lc and Lfare the number of hours Crusoe spends producing coconuts and sh respectively. Crusoe's utility mction from consumption is U(C, F) = CF. (a) Find Crusoe's production possibilities frontier. Find a formula for the marginal rate of transformation. (b) How many hours will Crusoe spend each day on each of the two production activities in order to maximize his utility? (Allow acrionaf quantities of goods to be produced.) (c) Show that, at the optimum you found in (b), the marginal rate of transformation is equal to the marginal rate of substitution. What price ratio would support this optimum as a competitive equilibrium