Jane has a budget of I dollars and is deciding how to invest over the three healthcare-related out-of- pocket spending categories: (1) preventive care, (2) dental care, and (3) chronic disease management. Denote the price of health investment in category 1, 2, and 3 as P1, P2, and P3 respectively; denote the quantity of health consumption in category 1, 2, and 3 as M1, M2, and M3, respectively. = . (a) Suppose the utility function of Jane is U(M4,M2,M3) = MaMM. Set up the Lagrange constrained optimization problem and write down the budget constraint. (b) Solve for Jane's optimal health investment quantity in category 1 (preventative care), 2 (dental care), and 3 (chronic disease management). (c) Provide an economic intuition of parameters a, b, and y. Jane has a budget of I dollars and is deciding how to invest over the three healthcare-related out-of- pocket spending categories: (1) preventive care, (2) dental care, and (3) chronic disease management. Denote the price of health investment in category 1, 2, and 3 as P1, P2, and P3 respectively; denote the quantity of health consumption in category 1, 2, and 3 as M1, M2, and M3, respectively. = . (a) Suppose the utility function of Jane is U(M4,M2,M3) = MaMM. Set up the Lagrange constrained optimization problem and write down the budget constraint. (b) Solve for Jane's optimal health investment quantity in category 1 (preventative care), 2 (dental care), and 3 (chronic disease management). (c) Provide an economic intuition of parameters a, b, and y