The final homework is Problems Sheet 4, Questions 4,5,7,8. (We have already done 6.) In all these questions the strategy is to use the necessary conditions of PMP to synthesize the optimal solution. What I mean by "synthesize" is that you write down all the information that PMP says is necessary (in terms of u(t) maximizing, H(x,u,\lambda) to -\lambda_0(t), and \dot \lambda=-\partial H/\partial x, and any boundary and transversality conditions) until you convince yourself that the optimal policy can only be one thing. Question 5 is a bit like proving the shortest distance between two points is a straight line. The answer is fairly obvious, but we can prove it is correct by applying the necessary conditions of PMP to rule out the possibility of any other solution.
Please send the solutions to me by next Monday.
Please send the solutions to me by next Monday.
