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

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Solution

(c) $2 x + y \geq 10$

We need to minimize the function Z = 6x + 10y

Converting the given inequations into equations, we obtain

$x = 6, y = 2, 2 x + y = 10, x = 0, y = 0$

These lines are drawn using a suitable scale

Scale
On X axis
1 Big division = 1 unit

On Y axis
1 Big division = 1 unit

The shaded region represents the feasible region of the given LPP.

We observe that the feasible region is due to the constraints $x \geq 6, y \geq 2$

So, the redundant constraint is $2 x + y \geq 10$

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Similar questions

Consider a LPP given by
Min Z = 6x + 10y
Subjected to x ≥ 6 ; y ≥ 2;
2x + y ≥ 10; x, y ≥ 0
Redundant constraints in this LPP are

Z = x + 2 y

x + 2 y \geq 100

2 x - y \leq 0

2 x + y \leq 200

x, y \geq 0

Z = x + 2 y

x + 2 y \geq 100

2 x - y \leq 0

2 x + y \leq 200

x, y \geq 0

z = 6 x + 10 y

x \geq 6, y \geq 2, 2 x + y \geq 10, x \geq 0, y \geq 0,

z = 5 x - 2 y

3 x + 2 y \leq 6, 10 x + 9 y \geq 45, x, y \geq 0

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