The utility that Corey obtains by consuming hamburgers (H) and steaks (S) is given by U(H,S) =H+(S+4) . The marginal utility of hamburgers is 0.5/H and the marginal utility of steaks is equal to 0.5/(S+4).

a)Sketch the indifference curve corresponding to the utility level U = 12.

b)Suppose that the price of hamburgers is $1 per hamburger, and the price of steak is $8 per steak. Moreover, suppose that Corey can spend $100 per month on these two foods. Sketch Corey's budget line for hamburgers and steak given this budget.

c)Based on your answer to parts (a) and (b), what is Corey's optimal consumption basket given his budget?