2. Jacob's preferences for goods X and Y can be described by U(X, Y) = X + 2Y + XY. Jacob has an income of $20 and faces prices Px = PY = $5. a. Use the Lagrangian method to derive Jacob's utility maximizing bundle given his budget constraint. (9 points) b. Now suppose Jacob's income falls to $5. Redo part a. You are not required to use the Lagrangian method for this part. (6 points) c. Calculate Jacob's MRS of X for Y at this new utility maximizing bundle. How does it compare to the MRT of X for Y? (3 points) d. On one graph, depict Jacob's utility maximizing bundles using indifference curves and budget lines, both before and after his income decreases. (7 points)