Solve for the optimal investment and capital profiles for the following problem by applying optimal control. I max / ert ak (t) - 301(t)2 dt sub. to K(t) = I(t), K(0) = Ko, K(T) free (i.e. no constraint on K (T) ), where r > 0 is the discount rate. The parameters a > 0, b > 0, and T > 0 are fixed