$w > 0$ and $m > 0$ are known and $w \ge m$. $\mu$ and $\lambda$ are known and $\mu > \lambda$.
\begin{align} \max_{H_t} & \, T \\ s.t. & \, \frac{dW_t}{dt} = \mu W_t - \mu H_t, W_T = 0, W_0 = w \\ & \, \frac{dM_t}{dt} = \lambda M_t - \lambda H_t, H_t - M_t \ge c, M_T = 0, M_0 = m \end{align}
I know the problem may be infeasible. How to solve the problem and characterize the corresponding feasible region in terms of $w$ and $m$.