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Linear Programming — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsLinear Programming1 Mark
Question
A constraint in an LP model becomes redundant because:
  1. Two iso - profit line may be parallel to each other
  2. The solution is unbounded
  3. This constraint is not satisfied by the solution values
  4. None of the above
✓

Answer

  1. None of the above

Solution:

A constraint in an LP model becomes redundant when the feasible region doesnt change by the removing the constraint.

For example, $\text{x}+2\text{y}\leq20$ and $2\text{x}+4\text{y}\leq40$ are the constraints.

$2\text{x}+4\text{y}\leq40$

$\Rightarrow2\times(\text{x}+2\text{y})\leq2\times20$

$\Rightarrow\text{x}+2\text{y}\leq20$

 which is same as the first constraint.

Therefore, $2\text{x}+4\text{y}\leq40$ can be removed.

By removing this constraint feasible region doesnt change.

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