1. In using the Solver package to solve a linear programming problem, the decision variables are assigned to the
A) target cell (or cells)
B) changing cell (or cells)
C) constraint cells
D) variable cells
2. In using the Solver package to solve a linear programming problem, the objective function expression and its value are defined in the
A) target cell (or cells)
B) changing (or cells)
C) constraint cells
D) variable cells
3. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained by multiplying the objective function of Problem A by a positive constant 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
Given
Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained by multiplying the objective function of Problem A by a positive constant and leaving all other things unchanged.
Problems A and B will have the same optimal solution but different objective function values
Correct option:
B) the same optimal solution but different objective function values
4. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained by multiplying the objective function of Problem A by a negative constant and leaving all other things unchanged. Problems A and B may 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.
5. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained by multiplying constraint 1 of Problem A by a positive constant 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
6. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained by multiplying all constraints of Problem A by a positive constant 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
7. 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 objective function 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
8. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained by multiplying constraint 1 of Problem A by a negative constant and leaving all other things unchanged. Problems A and B may 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
9. 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
10. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained from Problem A by omitting the non-negativity constraints 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 constraints in the solutions
11. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained from Problem A by omitting 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 constraints in the solutions
12. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained from Problem A by dropping exactly one variable 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 constraints in the solutions
13. Problem 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 £ 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
14. Problem A is a given formulation of a linear program with an optimal solution, and its constraint 1 is £ type. Problem B is a formulation obtained from Problem A by replacing the £ constraint with an equality constraint 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 constraints in the solutions
15. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained from Problem A by adding a redundant constraint, 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
16. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained from Problem A by adding a constraint, 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 Problem B