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Operation Research

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Operation Research
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

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