Given a linear controlled autonomous system, we consider the problem of including a con- vex compact set in the reachable set of the system in the minimum time and the problem of determin- ing the maximum time when the reachable set can be included in a convex compact set. Additionally, the initial point and the time at which the extreme time is achieved in each problem are determined. Each problem is discretized on a grid of unit vectors and is then reduced to a linear programming prob- lem to find an approximate solution of the original problem. Additionally, error estimates for the solu- tion are found. The problems are united by a common ideology going back to the problem of finding the Chebyshev center.