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Linear Inequalities

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Question : 4 of 54

Marks: +1, -0

Graphs of Inequations are drawn below :

L_{1}: x+2 y=1000 ; L_{2} x+y=800 ; L_{3}: x=400 ; L_{4} y=700

The shaded part shown in the diagram refers to:

$x+2 y \le 1000$
$x+y \le 800$
$x \le 400$
$y \le 700$
$x \ge 0, y \ge 0$
$x+2 y \ge 1000$
$x+y \le 800$
$x<400$
$y \le 700$
$x \ge 0, y \ge 0$
$x+2 y \le 100$
$x+y \ge 800$
$x \le 400$
$y \le 700$
$x \ge 0, y \ge 0$
none of these.

Solution:

Concept:

The shaded region is the intersection of half-planes determined by the given lines and the axes, based on the direction of shading.

Explanation:

The graph (not shown) typically has lines

L_1

,

L_2

,

L_3

,

L_4

forming a boundary, with the shaded region below all lines and bounded by the axes.

This implies each inequality is of the "less than or equal to" type:

x+2y \le 1000

,

x+y \le 800

,

x \le 400

,

y \le 700

, and

x \ge 0, y \ge 0

for the axes.

Option A matches exactly these constraints.

Answer:

Option A

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