Solving an integer programming problem by rounding off answers obtained by solving it as a linear programming problem (using Simplex LP), we find that

Solving an integer programming problem by rounding off answers obtained by solving it as a linear programming problem (using Simplex LP) can lead to suboptimal or even infeasible solutions. Here's why:

1. Linear Programming (LP) and Integer Programming (IP) are two different mathematical optimization techniques. LP allows for continuous decision variables, while IP requires some or all decision variables to be integers.

2. The Simplex method is a popular algorithm for solving LP problems. It works by moving along the edges of the feasible region (defined by the constraints) to find the optimal solution.

3. If you solve an IP problem as if it were an LP problem, you might end up with non-integer decision variables. Rounding these off to the nearest integer might seem like a logical step, but it can lead to problems.

4. Rounding off can lead to suboptimal solutions. The optimal solution to the LP problem is not necessarily the optimal solution to the IP problem. By rounding off, you might be moving away from the true optimal solution of the IP problem.

5. Rounding off can also lead to infeasible solutions. The rounded-off solution might not satisfy all of the original constraints of the IP problem.

6. Therefore, while the Simplex method can provide a good starting point or an initial solution for an IP problem, rounding off the solution is not a reliable method for solving IP problems. Specialized techniques, such as branch and bound or cutting plane methods, are typically used to solve IP problems.