Assume that an individual consumes three goods, 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, $8, $9, and $10. The total income of the consumer is $144, and the marginal utility schedule is as follows: Units of Marginal Marginal Marginal good utility of X utility of F utility of Z 50 36 120 45 33 100 40 30 80 35 27 60 30 24 40 24 21 30 20 18 25 15 20 5 12 15 10 9 10 a. Given a $144 income, how much of each good should the consumer purchase to maximize utility? What is her total utility? b. Suppose income rises to $254 with the same set of prices; what combination will the consumer choose? What is her total utility? c. Let income fall to $30 and prices remain the same. How does the consumer allocate income now? What is her total utility? d. Given the solution in part c, what would you say if the consumer maintained that X' and Y' are not purchased because she could no longer afford to buy X or Y