Suppose you're headed on a vacation, and are beginning to pack. In particular, consider your decision about how much shampoo (x) and conditioner (y) to pack. Your utility is u(x, y) = min{xr, 3y}. In order to save money, you've decided to not check a bag, so the amounts of x and y you take are limited by security regulations. Let the prices be pz = 5, Py 10, and let your income be M = 200. Additionally, let the amount of liquids you're allowed to take on the plane be L = 33 ounces. A bottle of shampoo takes up 3 ounces, and a bottle of conditioner takes up 2 ounces. How many bottles of shampoo and conditioner will you take with you? (You can assume that it is possible to take a fraction of a bottle.)