Problem A is a given formulation of a linear programming problem with an optimal solution. Problem B is a formulation obtained from problem A by adding a constant value to the right hand side of constraint $1$ of problem A and leaving all other things unchanged. Problem A and B will have

Question $11$ options:

Same or different solution profile depending on the role of the constraint in the solutions

The same optimal solution but different objective function values

Different optimal solutions and different objective function values

The same optimal solution and same objective function value

Different optimal solutions but same objective function value