Jane has a utility function U=10X0.4Y0.6, where the quantity consumed per day of water is X and food is Y. The price of water is $0.80 per unit and the price of food is $3.20. The budget constraint for food and water together is $20 per day. (a) Derive equations for the marginal utility of water (MUX) and the marginal utility of food (MUY). In one sentence, explain what the marginal utility of water means. (3 marks) (b) Derive an equation for an indifference curve with Y in terms of X when U=50. (2 marks) (c) The maximum quantity of water that Jane can afford with zero food is Max(X), and the maximum quantity of food with zero water is Max(Y). Calculate Max(X) and Max(Y) (2 marks) (d) Solve for the optimum quantity of food and water that Jane prefers to consume. At the optimal solution, what percentage of the budget is spent on (i) water and (ii) food? (3 marks) Jane has a utility function U=10X0.4Y0.6, where the quantity consumed per day of water is X and food is Y. The price of water is $0.80 per unit and the price of food is $3.20. The budget constraint for food and water together is $20 per day. (a) Derive equations for the marginal utility of water (MUX) and the marginal utility of food (MUY). In one sentence, explain what the marginal utility of water means. (3 marks) (b) Derive an equation for an indifference curve with Y in terms of X when U=50. (2 marks) (c) The maximum quantity of water that Jane can afford with zero food is Max(X), and the maximum quantity of food with zero water is Max(Y). Calculate Max(X) and Max(Y) (2 marks) (d) Solve for the optimum quantity of food and water that Jane prefers to consume. At the optimal solution, what percentage of the budget is spent on (i) water and (ii) food