If you are solving a mixed-integer programming problem (any problem with integer constraints) using Analytic Solver or a subset product (Analytic Solver Optimization, Analytic Solver Upgrade or Analytic Solver Basic) with a non-zero value for the integer Tolerance setting in the Integer section of the Task Pane Engine tab, the Branch & Bound method has found a solution satisfying the constraints (including the integer constraints) where the relative difference of this solution’s objective value from the true optimal objective value does not exceed the integer Tolerance setting.  (For more inform­ation, see “Integer Section of the Engine Tab Options” in the chapter “Solver Engine Option Reference.”)  This may actually be the true integer optimal solution; however, the Branch & Bound method did not take the extra time to search all possible remaining subproblems to “prove optimality” for this solution.  If all subproblems were explored (which can happen even with a non-zero Tolerance in some cases), Analytic Solver will produce the message “Solver found a solution.  All constraints are satisfied” (result code 0, shown earlier in this section).