3. Joseph has the utility function U(F, H) = 10F2H, where F is the quantity of food he consumes per week and H is the quantity of housing per week. Suppose the price of food is $10 and the price of housing is $5, while Joseph has an income of $150/week. (use food on X-axis and housing on Y- axis) a. Write Joseph's budget constraint. b. Calculate Joseph's MRS as a function of the quantities F and H. C. Write out Joseph's constrained optimization problem c. Using the Lagrangian method, solve for Joseph's optimal consumption bundle of food and housing. d. Now suppose that price of food has increased to $15. Using MRS and MRT relationship at the optimal, calculate new consumption bundle of food and housing. 4. Consider Jen, a consumer with preferences U(F, H) = F1/3H2/3, where H is the quantity of housing and F is the quantity of food (per month). Suppose Jen has a stipend of $600/month which she uses to purchase food at a price of $1/unit and housing at a price of $10/unit. (use food on X- axis and housing on Y-axis) Compute Jen's utility-maximizing bundle of goods