Please write clearly, Thanks!

1. (35 points) Solve the following dynamic optimization problem using the method of optimal control: 00 minf (KW$2 + 2n; 112 + ijdt 0 subject to 13' = :.." 21:. + 1, where 53(0) = 1:0. Let m(t] be the current value multiplier. (a) Find the steady state and the optimal path in a phase diagram. Please put aft) on the horizontal axis and m(t) on the vertical axis in the phase diagram. (h) Calculate the optimal :r(t) and m{t] analytically. {There is no need to nd the constants of integration.) (c) In a phase diagram, show the eect of a sudden increase in s" when the system was in the steady state