Please use hamiltonian

Problem 5 (30 points). Consider the following optimal control problem: 1 max (ty (1?) % (u(t))2) dt \"(331318) 0 subject to y(t] = 11505), 7.56) E R, 9(0) 2 07 y(1) is free. (a) (5 points) Write down the necessary conditions for optimality. (b) (7 points) Solve for the optimal u (t), y (t) and A (t). (c) (9 points) Now suppose that we have y (1) = 0 instead of free y(1). Solve for the optimal u (t), y (t) and A (t). (c) (9 points) Now suppose that once again we have free y [1)j but there is a new restriction u (t) g l for every t E [0, 1]. Solve for the optimal u (t), y (t) and A (t)