Consider the utility maximization problem subject to a budget constraint: 3, s.t. x+2. y=80 (r, y are nonnegative). (a) Solve the problem above, i.e. find the best combination of goods x and y that the consumer should choose. What is the value of the Lagrange multiplier? (b) Use the 2nd-order conditions to show that the combination found in part (a) is indeed optimal. (c) Suppose the income decreases from 80 to 79.5. Estimate the effect of this on the utility level of the consumer using the Lagrange multiplier found in part (a). max