In this paper we apply PDE methods to solve a problem about minimizing the cost of a firm for operating a project which is a simple model of combined singular stochastic control and optimal stopping in finite horizon. The value function V (x, t) to the problem is governed by a time-dependent HJB variational inequality with both gradient constraint and function constraint which leads to a time-dependent stopping boundary and a moving boundary. We will prove that two free boundaries are strictly monotonic and infinitely differentiable. V, partial derivative V-x, partial derivative V-t are continuous, and partial derivative V-xx is locally bounded. Based on these results we construct optimal control and optimal stopping.