Inequations involved in the given region are____________? - Vidyadip

MCQ

Inequations involved in the given region are____________?

A
$2\text{x}+\text{y}\geq6,\text{x}\geq0,\text{y}\geq0$
B
$2\text{x}+\text{y}>,\text{x}\geq0,\text{y}\geq0$
C
$2\text{x}+\text{y}<6,\text{x}\geq0,\text{y}\geq0$
D
$2\text{x}+\text{y}\leq6,\text{x}\geq0,\text{y}\geq0$

✓

Answer

$2\text{x}+\text{y}\leq6,\text{x}\geq0,\text{y}\geq0$

Solution:

Since region involves 1^st quadrant so $\text{x}\geq0,\text{y}\geq0.$

Two points on line are $(0,6)$ and$(3,0)$

$\frac{(\text{y}-6)}{(0-6)} =\frac{(\text{x}-0)}{(3-0)}$

$\Rightarrow\frac{(\text{y}-6)}{(-6)}=\frac{\text{x}}{3}$

$\Rightarrow\text{y}-6=2\text{x}\Rightarrow2\text{x}+\text{y}=6$

$2\text{x}+\text{y}\leq6$ since $(0,0) $ should also satisfy.

So, $ 2\text{x}+\text{y}\leq6, \text{x}\geq0, \text{y}\geq0.$

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