(a) Suppose we have preferences U(X, Y) = min [2X, Y]. Graph/sketch the indifference curve through the bundle X = 10 and Y = 10. What is the utility at (10, 10)? Explain why the indifference curve looks the way it does. (b)What do we mean by a composite good? What does this composite good look like with these preferences? Show and explain. (c)Let Px = $10, Py = $20 and income M = $600. State the consumer's maximization problem and express this in words. (d)Find optimal X, Y, and the resulting Utility. Explain how you get the optimum and show/sketch in a figure. (e)Now suppose we offered a discount so that good Y was priced at $5 for the first 10 units but rises to $10 for any quantity above that. Draw the new budget line. (f)Find the optimal X. Y and the resulting Utility given the availability of the discount. Compare to the non-discounted case and discuss why it is different the same