Problem $A$ Is a Given Formulation of a Linear Program with an with an Optimal

Multiple Choice

Problem $A$ is a given formulation of a linear program with an optimal solution. Problem $B$ is a formulation obtained by adding a constant to the right hand side of Constraint 1 of Problem A and 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 constraint in the solutions