Suppose that Monica has income of $120, and faces prices PX= $2 and PY = $3, where X= number of cups of coffee and Y=number of cupcakes. Her goal is to maximize her utility, described by the function U = 10X0.5Y0.5. a) Represent graphically the problem Monica faces. Make sure you identify your axes as well as your budget constraint and indifference curves. Also identify the optimal bundle. b) Calculate the optimal bundle. Make sure you show all your calculations. c) Calculate the point price elasticity of demand at the optimal bundle. Make sure you show all your calculations. d) Represent on a graph Monica demand function for cups of coffee. e) Is coffee a normal good? Justify your answer and show all your calculations