Question

Solving an integer programming problem by rounding off answers obtained by solving it as a linear programming problem (using simplex), we find that
A) The values of decision variables obtained by rounding off are always very close to the optimal values.
B) The values of the objective function for a maximization problem will likely be less than that for the simple solution.
C) The values of the objective function for a minimization problem will likely be less than that for the simplex solution.
D) All constraints are satisfied exactly.
E) None of the above.

Answer 1

Hint: Use the concept of finding the basic feasible solution of an integer programming problem by using the simplex method and then determine the optimal solution for the given problem.

Complete step by step solution: As we know to find the maximum or minimum value of the objective function we used to solve it for an initial basic feasible solution by the simplex method.
For this, so we will convert the problem into the standard form which involves objective function and constraints equations in terms of x and y whose values we will determine from the initial basic feasible solution and using it further when we will get the optimization problem we will see that the value of the objective function for a maximization problem will likely be less than that for the simplex solution.

Hence, the correct option is (B).

Note:Some other important points are:
1) The values of the decision variables generally are not very close to the optimal values.
2) The values of the objective function will not likely be less than the simplex solution in case of a minimization problem.