11. Assume that an individual consumes three go|ods, X, Y, and Z. The marginal utility (assumed measurable) of each good is independent of the rate of consumption of other goods. The prices of X, Y, and Z are, respectively, $1, $3, and $5. The total income of the consumer is $65, and the marginal utility schedule is as follows: Marginal Marginal Marginal Units of utility of X utility of Y utility of Z good (units) (units) (units) 1 12 60 70 2 11 55 60 3 10 48 50 4 9 40 40 5 8 32 30 6 7 24 25 7 6 21 18 8 5 18 10 9 4 15 3 10 3 12 1 a. Given a $65 income, how much of each good should the consumer purchase to maximize utility? b. Suppose income falls to $43 with the same set of prices; what combination will the consumer choose? c. Let income fall to $38; let the price of X rise to $5 while the prices of Y and Z remain at $3 and $5. How does the consumer allocate income now? What would you say if the consumer maintained that X is not purchased because he or she could no longer afford it