Question

Consider a LPP given by

Minimum Z = 6x + 10y

Subjected to x ≥ 6; y ≥ 2; 2x + y ≥ 10; x, y ≥ 0

Redundant constraints in this LPP are

A. x ≥ 0, y ≥ 0

B. x ≥ 6, 2x + y ≥ 10

C. 2x + y ≥ 10

D. None of these

Answer 1

Correct answer is C.

Given

Objective Function is Z = 6x + 10y

Constraints are:

x ≥ 6

y ≥ 2

2x + y ≥ 10

x, y ≥ 0

A redundant constraint is that, which doesn’t intersect with the feasible region of the out non-redundant constraints.

Here, the problem is a minimization problem and as per the constraints x ≥ 0 and y ≥ 0 the feasible solution is located in the 1^st quadrant.

Now, if we map all the three inequalities in a graph, we have

From the graph, it is very clear that, the graph of the inequality 2x + y ≥ 10 is not intersecting the feasible region formed by the constraints x ≥ 6; y ≥ 2; x ≥ 0 and y ≥ 0.

Hence the inequality 2x + y ≥ 10 is not really making any difference to the feasible region from by x ≥ 6; y ≥ 2; x ≥ 0 and y ≥ 0.

Therefore inequality 2x + y ≥ 10 remains redundant.