A. Alice consumers two goods, at and 3;. Her utility function is U(x, y) =10ln(23: + 23;) + 2y. The prices for :r and y are pm and 3),, (in dollars per unit), respectively. Alice has an income of m dollars. Find Alice's optimal bundle as a function of pm, 303,, and m. [Hint: Be aware of corner solutions!] [Recall that MUth'y) = ($133,) and MUy|{1,y} = {$ny + 2.] B. Bob likes to have the same amount of a: as he has of y. His utility function is may) = min{2:r + y, 2y + 2:}. 0 Draw Bob's indifference curves that pass through the bundles ( 10, 5) and (4, 8). 0 Bob has an income of $100 and px = 10. Find Bob's optimal bundle as a function of Py- C. Carol consumes 2 goods, 2: and 3;. Her utility function is U(zr, y) = 4min{zr, y} + y. Let pm and 3),, denote the prices of goods 2: and 3;, respectively, and let in denote Carol's income. 0 Draw Carol's indifference curve that passes through the bundle (5, 5). 0 Find Carol's (Marshallian) demand functions for a: and y (as a function of pi, pg, and 0 Draw Carol's Engle curves for :r and y when px = 1),, = 1 and when px = 5, p3, = l. 0 Draw Carol's demand curve for 2: when p3, = 1 and m = 10 and draw Carol's demand curve for y when 101 = 8 and m = 40. D. Dan's utility function is U(:r, y) = 4ln:r +y, where as is his consumption of good 3 and y is his consumption of good 3;. Let p3 and 10,, denote the prices of goods 1: and 3;, respectively, and let an denote Dan's income. [Note that MM\