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Linear Programming — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsLinear Programming1 Mark
Question
In Graphical solution the redundant constraint is:
  1. Which forms the boundary of feasible region.
  2. Which do not optimizes the objective function.
  3. Which does not form boundary of feasible region.
  4. Which optimizes the objective function.
✓

Answer

  1. Which does not form boundary of feasible region.

Solution:

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

For example, $2\text{x}+\text{y}\geq10$ and $6\text{x}+3\text{y}\geq30$ are constraints.

$6\text{x}+3\text{y}\geq30$

$\Rightarrow3\times(2\text{x}+\text{y})\geq3\times10$

$\Rightarrow2\text{x}+\text{y}\geq10$

 which is same as the first constraint.

Therefore, $6\text{x}+3\text{y}\geq30$  can be removed.

By removing this constraint the feasible region doesnt change.

If the boundary of the feasible region is removed then feasible solution set changes.

Hence, redundant constraint cannot be the boundary of the feasible region.

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