Test Index

Linear Inequalities

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Question : 8 of 54

Marks: +1, -0

Graphs of the Inequations are drawn below :

L_{1}: 3 x+3 y=36 ; L_{2}=5 x+2 y=50 ; L_{3}: 2 x+6 y=60 ; x \geq 0, y \geq 0

The shaded region M O D E F shown in the figure 8.20 refers to the inequalities:

$3 x+3 y \leq 36$
$2 x+6 y \geq 60$
$5 x+2 y \leq 50$
$x \geq 0, y \geq 0$
$3 x+3 y \leq 36$
$2 x+6 y \leq 60$
$5 x+2 y \leq 50$
$x \geq 0, y \geq 0$
$3 x+3 y \geq 36$
$2 x+6 y \leq 60$
$5 x+2 y \geq 0$
$x \geq 0, y \geq 0$
none of the above.

Solution:

Concept:

The shaded region is the intersection of half-planes determined by the given lines and the axes.

Explanation:

The region includes the origin

O(0,0)

because the origin satisfies

x \ge 0

,

y \ge 0

and all three inequalities when taken as "less than or equal to".

Check origin for each line:

3(0)+3(0)=0 \le 36

,

2(0)+6(0)=0 \le 60

,

5(0)+2(0)=0 \le 50

.

Thus the feasible region is bounded by the three lines and the axes, corresponding to all three inequalities being

\le

.

Option A has

2x+6y \ge 60

which excludes the origin, and option C has

3x+3y \ge 36

which also excludes the origin. Only option B includes the origin and gives a bounded region.

Answer:

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