Consider an equation of motion of dx/dt=2x(1x/100)y where x is the stock and y is the control variable (each is a function of time). Each period's objective is given by 10y(1/20)y2 and the discount rate is 10%.

1. Indicate the (continuous-time) Hamiltonian and conditions of the maximum principle.
2. Draw a phase-plane diagram including isoclines and directionals for each region.