2- Consider the following problem max I 010(211 + y)dt, subject to the following conditions: ll. 3" = u + y, 31(0) = 6, u E [0,1] and the terminal value of the state variable has to be at least 15. a) Write down the optimality conditions (5 Marks) b) Find the optimal trajectories of consumption (q), pollution stock (S) and shadow price (/1 ) (15 marks)