Problem 6 (20 points) A consumer purchases two goods, 2 and y. His utility function is: ((c. v) =21() + 1(2 + 2). Suppose that the price of a is 2, the price of y is 1, and the consumer's income is 10. Thus, the consumer chooses a and y to maxinise ( (r, y), subject to z and y satisfying his budget constraint, 2r - y = 10. a (5 points). Use the Lagrangian method to find the utility-maximising values of z and y b (5 points). What is the value of the Lagrangian multiplier J? e (5 points). What is the consumer's maximised utility? d (5 points). Now suppose that the price of good * increases to 4. That is, the new budget constraint is Ar by = 10. What are the new utility-maximising values of a and y