Consider a dynamic optimization problem the objective of maxt=0e0.1t(3y5+6yx112y2)dt subjective to the equation of motion dx/dt=24x/10y

1. Indicate the (continuous time) Hamiltonian and conditions of the maximum principle .
2. Draw a phase-plan diagram including isoclines and directionals for each region. Sketch in approximate approach paths to the equilibrium.
3. Consider the equation of motion of questions 1 and 2 but where there is no optimization. Instead, the change in y is given by dy/dt=5/3+x/6y/12. Draw a phase-plan diagram indicating the isocline (i.e. dy/dt=0 and dx/dt=0) and the directionals for each region. Note that there are might no longer be a unique approach path.