Problem 2: Maximizing utility with perfect substitutes. (40 pts) Bill likes both Red Bull (331) and Monster (332) energy drinks. Both help him stay awake to nish his microeconomics homework, so they're perfect substitutes in that sense (though Monster cans are larger). His preferences over the drinks can be represented by utility function U031, $2) = 5131 + 4332. (3.) Suppose the price of Red Bull is p1 = $2.50 per can and the price of Monster is 132 = $2. Write down Bill's budget constraint if his income is $50. Graph the budget line and some representative indifference curves. (b) What's Bill's optimal (:51, 3:2) choice given his preferences, income, and the prices of the two goods. (c) What is the value of Bill's utility at this utility maximizing choice? (d) Monster is running a major promotion and is selling for $.50 a can. What is Bill's new consumption choice? (e) What is the new value of Bill's utility at this utility maximizing choice