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4. A consumer receives utility (1,402) from consuming two goods 1,12. The consumer always prefers more of these goods, but she is constrained by her budget pha + P239 = m. Therefore, she solves the problem 1/2_3/4 max (01.02) = subject to Pin + P232 = m where Pi, Pa are the prices of 1,2 respectively and m is her income. (a) Set up the maximization problem using the substitution method (that is, solve the budget con- straint for one of the variables and substitute that expression into the utility function). Write down the first order condition for this problem. 6PTS (b) Set up the maximization problem using a Lagrange multiplier (see section 14.1). Write down the first order conditions for this problem. 6PTS * (c) Solve for x* and r*