If you add one or more new constraints to a linear program, the value of the obj

Question

If you add one or more new constraints to a linear program, the value of the objective function at optimality can potentially improve, depending on the specifics of the new constraints. If the feasible region of a linear program is unbounded, then the value of the objective function must go to either infinity or negative infinity. Divisibility, as one of the assumptions of LP, says that you must be able to divide one decision variable by another decision variable in the objective function and in the constraints. Proportionality, as one of the assumptions of LP, says that the contribution a decision variable makes to the objective function and to each constraint is proportional to the value of the variable. In the Simplex method the number of basic variables is, by definition, always equal to the number of decision variables in the LP model.

Explanation / Answer

1)

If you add a constraint to a problem, two things can happen. The area of the feasible region decreases or remains the same . If the original solution satisfies the new constraint then the solution remains the same. If the original solution does not satisfy the new constraint, then the new problem is feasible or infeasible. If feasible , the region becomes small ,the value must go down (F).

2) The feasible feasible region of an LPP is unbounded does not imply that there is no optimum. Optimality depends on the property of objective function

for example consider

Min x+y

such that x>=0,y>=0

Then minimum exists at x=y=0 and minimum value is 0. But the region is unbounded

Also Max x+y cannot find

answer: (F)

3) Divisibility means that  the decision variables can take on fractional (non-integer) values. We cannot divide a decision variable with another. Then the problem becomes non - linear

answer : (F)

4)Proportionality means that each decision variable in every equation must appear with a constant coefficient. In the objective function, proportionality implies that the the contribution to the objective and constraints for each variable is assumed to remain constant throughout the entire range of activity levels in the problem. (T)

5)

For a system of m simultaneous linear equations in n unknowns (n> m), a solution obtained by setting any n-mvariables equal to zero and solving for remaining m variables, provided the determinant of the coefficients of these m variables is non-zero is called a basic solution. Such m variables (some of them may be zero) are called basic variables and remaining n-m zero valued variables whose values did not appear in the solution are called non-basic variables

number of basic variables = number of equations not the decision variables (F)

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.