2. (25 points) An individual plans the upcoming year. They maximise utility 3 u(c,v) = (C32 + 0%) 2 by choosing how much consumption (3 to have and how many months I) of vacation to take. Time is spent either on vacation or working for a monthly salary of 5. Labour income is completely spent on consumption, where each unit of consumption costs p. a) (4 points) Formally write the constrained optimisation problem, not ing thatO g '0 S 12. b) (8 points) Identify all cases implied by complementary slackness, as well as their implied equations and checks. c) (10 points) What is the optimum consumption amount 0 and vacation amount '0? d) (3 points) Suppose the monthly salary increases while the price of consumption stays constant. What happens the to optimal months of vacation? Justify your answer mathematically