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In solving the following Linear Programming Problem, ''minimise f = 6x + 10y subject to x ≥ 6; y ≥ 2; 2x + y ≥ 10; x ≥ 0; y ≥ 0'', the redundant constraint(s) is/are:
  • a)
    x ≥ 6, y ≥ 2
  • b)
    2x + y ≥ 10, x ≥ 0, y ≥ 0
  • c)
    x ≥ 6
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
In solving the following Linear Programming Problem, ''minimise f = 6...

Explanation:

Redundant Constraints in Linear Programming:

In linear programming, a constraint is considered redundant if it does not affect the feasible region of the problem. In other words, removing a redundant constraint will not change the feasible region or the optimal solution of the problem.

Analysis of Constraints:

Given constraints:
1. x ≥ 6
2. y ≥ 2
3. 2x + y ≥ 10
4. x ≥ 0
5. y ≥ 0

Let's analyze each constraint to identify the redundant one(s).

1. x ≥ 6, y ≥ 2:
These constraints are necessary as they define the lower bounds for x and y.

2. 2x + y ≥ 10, x ≥ 0, y ≥ 0:
The constraint 2x + y ≥ 10 is essential as it directly affects the feasible region. However, the constraints x ≥ 0 and y ≥ 0 are non-redundant basic constraints for any linear programming problem. These constraints ensure that x and y are non-negative.

Conclusion:

Therefore, the redundant constraint(s) in the given linear programming problem is option B) 2x + y ≥ 10, x ≥ 0, y ≥ 0. Removing these constraints will not alter the feasible region or the optimal solution.
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Community Answer
In solving the following Linear Programming Problem, ''minimise f = 6...
For x ≥ 6, y ≥ 2; 2x + y ≥ 2 × 6 + 2; hence, the constraint 2x + y ≥ 10 is automatically satisfied by every point of the graph of the inequalities x ≥ 6 and y ≥ 2. Also, the graph of x ≥ 6 and y ≥ 2 is a subset of the graph of the inequalities x ≥ 0 and y ≥ 0.
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In solving the following Linear Programming Problem, ''minimise f = 6x + 10y subject to x ≥ 6; y ≥ 2; 2x + y ≥ 10; x ≥ 0; y ≥ 0'', the redundant constraint(s) is/are:a)x ≥ 6, y ≥ 2b)2x + y ≥ 10, x ≥ 0, y ≥ 0c)x ≥ 6d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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