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2. Suppose a consumer derives utility from consuming two goods, :31 and 3:2. Her utility function is given as U(s:1,:1:2) 2 84:31:32. The consumer must pay $20 for good 1 and $15 for good 2. The consumer's monthly income is $6, 000. a. Determine the optimal quantities of 3:1 and :32 the consumer should purchase in order to maximize their utility. b. What is the maximum level of utility the consumer receives? c. Plot in the goods space the budget constraint and the indifference curve representing the maximum utility attained in this problem. Also indicate the optimal consumption combination, as well as the values of the slope and intercepts associated with the budget constraint