Please prepare answers to the questions below. These questions are pit I. CONSUMER UTILITY (20 points) A consumer's utility function is U(x, y) = xy + 10x, where x is the quantity of good x consumed and y is the quantity of good y consumed, The prices of the two goods are p. and p, and the consumer has total income of I. a. Set up the Lagrangian expression to solve for the consumer's optimum consumption bundle. Show the equations for the first order conditions. b. What, in general, must be true for the consumer to be maximizing utility? c. Show the exact expressions for the marginal rate of substitution, for the slope of the budget constraint, and for the tangency condition that determines the consumer's optimal choices. Note: You do NOT need to explicitly solve for x and y. d. Illustrate the consumer's optimal choice on an x, y graph