Assume a consumer's utility function for goods x and x2 is of the following form: 2/3 1/3 U(x1, X2) = X1 X2 Next, assume p1 = 1, p2 = 1, and Y = 120. a. Find the expressions for the consumer's marginal utility with respect to both x, and x2 (MU1 and MU2). b. Use your answer from part (a) to find the marginal rate of substitution (MRS) if the consumer had 100 units of x1 and 20 units of x2. c. Write the equation for the consumer's budget constraint. d. Set up the Lagrangian function. e. Find the first-order conditions. f. Solve the first-order conditions for the optimal bundle of x1 and x2