Question: Consider a utility-maximizing consumer who devotes all of his weekly income, I = $720 to purchases of caviar (available at the market price, px = $10 per serving) and high-end denim jeans (available at the market price py=$120 per pair). Compute this consumer's optimal consumption of caviar (x) and jeans (y) for each of the following possible utility functions, and show your work:
a. U (x,y) = [2x +13y]^2
b. U(x,y) = Min [x,6y]
c. U(x,y) - xy^2