Problem $\mathrm{A}$ is a given formulation of a linear program with an optimal solution and exactly one equality constraint. Problem B is a formulation obtained from Problem A by replacing the equality constraint with a pair of inequality constraints obtained by serially replacing the equality sign of the constraint with $\pounds$ and ${ }^{3}$ signs, leaving all other things unchanged. Problems A and B will have
A) the same optimal solution and same objective function value
B) the same optimal solution but different objective function values
C) different optimal solutions but same objective function value
D) different optimal solutions and different objective function values
E) same or different solution profile depending on the role of the constraints in the solutions

Question

Quizplus · Accepted Answer

Replacing an equality constraint with a pair of inequality constraints that represent the same equality (one inequality for $\leq$ and one for $\geq$) does not change the feasible region or the optimal solution of a linear program, assuming all other aspects of the problem remain unchanged. Therefore, Problems A and B will have the same optimal solution and the same objective function value.

Problem A\mathrm{A}A Is a Given Formulation of a Linear Program with an with an Optimal

Problem $\mathrm{A}$ Is a Given Formulation of a Linear Program with an with an Optimal