Question

The shaded region shown in the figure is given by the inequation

• A. $14x+5y\ge 70y\le 14\text{and}x-y\le 5$
• B. $14x+5y\ge 70y\le 14\text{and}x-y\ge 5$
• C. $14x+5y\le 70y\le 14\text{and}x-y\ge 5$
• D. $14x+5y\ge 70y\ge 14\text{and}x-y\ge 5$

Answer 1

The correct option is A $14x+5y\ge 70y\le 14\text{and}x-y\le 5$

Using two point equation of the line
equation of the line passes through $(0,14),(19,14)$ is $y=14$
and $(5,0),(19,14)$ is $x-y=5$
and $(5,0),(0,14)$ is $14x+5y=70$
Seeing the image the origin lies below the line in case of $y=14$ so the inequation is $y\le 14$
in case of $x-y=5$ origin lies above the line so the inequation is $x-y\le 5$
and in case of $14x+5y=70$ origin lies above the line so the inequation is $14x+5y\ge 70$