# Operation Research

Topics: Optimization, Linear programming, Dual problem Pages: 2 (412 words) Published: June 14, 2012
1) What is the meant by the term ‘feasible region’?
Its feasible region is a convex polyhedron, which is a set defined as the intersection of finitely many half spaces, each of which is defined by a linear inequality.

2) What is an infeasible solution? How is this condition recognized in simplex method? A infeasible solution is one that does not satisfies all linear and non-linear constraints. When the solution is along with the artificial variable even when the aolution is optimized then its is a infeasible solution

3) What is an unbounded solution? How is this condition recognized in simplex method? A linear program is unbounded if the optimal solution is unbounded, i.e. it is either ∞ or −∞. In simplex when the

entry values are negative its solution is unbounded.

4. Define slack and surplus variables in a LPP?
a slack variable is a variable that is added to an inequality constraint to transform it to an equality.
In Linear programming a surplus variable is a variable which is subtracted from a constraint to turn the inequality into an equation. This is required to turn an inequality into an equality where a linear combination of variables is greater than or equal to a given constant in the former..

5.What are the artificial variables?
One type of variable introduced in a linear program model in order to find an initial basic feasible solution; an artificial variable is used for equality constraints and for greater-than or equal inequality constraints. 6.Define optimal basic feasible solution?

An optimal solution to a linear program is a feasible solution with the largest objective function value (for a maximization problem). The value of the objective function for the optimal solution is said to be the value of the linear program.

7.Define the dual of a LPP?
Linear programming in which the maximum and minimum number are the same number.
8.What is the principle of duality in LPP?
the duality principle states that...