1. 0n the planet Mela ncholia, consumers minimize utility subject to an equality income constraint as well as nonnegativity constraints. (Other than that, things are the same for an individual Melancholian as here on Earth: assume n goods; that the utility function is strictly quasiconcave, continuous, and maps the consumption set X into R; X is a subset nn of R that is nonempty, convex, closed, and 0 ex; y 61R; and p 6R.) We ++++ established in class that the consumers here on Earth have a consumption bundle which maximizes their utility subject to their budget constraint. Do Melancholians necessarily have a consumption bundle which minimizes their utility subject to their budget constraint? Carefully demonstrate that your answer is correct. (Hint: This is not asking you to characterize the optimum in any way, just show that the optimum exists.)