What kind of constraint can be added or deleted from a linear programming model without changing the feasible region?

Option 1 : There will be no effect

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15 Questions 15 Marks 12 Mins

Explanation:

• Linear programming (LP) in industrial engineering is used for the optimization of our limited resources when there is a number of alternate solutions possible for the problem. The real-life problems can be written in the form of a linear equation by specifying the relation between its variables.  
• The general LP problem calls for optimizing a linear function for variables called the "objective function" subjected to a set of linear equations and inequalities called the constraints or restriction.
• A redundant constraint is a constraint that can be removed from a system of linear constraints without changing the feasible region.
• While solving a linear programming model, if a redundant constraint is added, then there will be no effect on the existing solution​.

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• Consider the following linear inequality constraints:

x = x1 and y = x2

1. 2x +1y ≤ 8,
2. 4x + 0y ≤ 15,
3. 1x + 3y ≤ 9,
4. 1x + 2y ≤ 14,
5. 1x ≤ 4, 
6. 1x + 1y ≤ 5,

where, x + y ≤ 0

Methods for Identification of Redundant Constraints 

Many methods are available in the literature to identify the redundant constraints in linear programming problems. In this paper, the following five methods are discussed and compared

1.  Bounds method 
2.  Linear programming method
3.  Deterministic method
4.  Stojkovic and Stanimirovic method
5.  Heuristic method

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