Problem 1 [20 points]. Wilma and her sister Wendy consume only toads and snakes. They make stew out of these ingredients using strict proportions, but each sister has her preferred recipe. Specifically, Wilma's preferences for toads (t) and snakes (s) can be described by utility function us1 (t, s) = min {t, s), while Wendy's preferences have the following utility function representation: Us2 (t, s) = min {2t, s}. Suppose also that they can purchase toads and snakes at respective prices pt > 0 and ps > 0, and joint wealth w > O to spend on both goods. 1) [6 points] Set up Wilma's utility maximization problem and derive her Marshallian demand correspondence, assuming she gets to spend all of their joint wealth. 2) [6 points] Set up Wendy's utility maximization problem and derive her Marshallian demand correspondence. 3) [8 points] Suppose that over time the sisters realize that they've developed a joint taste for a different recipe. That is, they now always maximize the following joint utility function: 1 1 U(t, s) = = min{t, s} + 5 min {2t,s} Set up the utility maximization problem of this household and derive the Marshallian demand correspondence