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Katie's utility function is U(X, Y)=3XY+6X. The price of good X is $1, the price of good Y is $5. a. (12pt) Suppose Katie has income |=$100 to spend on good X and good Y. Solve Katie's utility maximization problem using a Lagrangian and find the optimal amount of X and Y she will consume. b. (6pt) Find Katie's Engel Curve for good X. Hint: Use a generic | instead of I=$100. c. (2pt) Is good X a normal good or an inferior good? Explain