Question

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

• A. $14x+5y\ge 70,y\le 14$ and $x-y\ge 5$
• B. $14x+5y\le 70,y\le 14$ and $x-y\ge 5$
• C. $14x+5y\ge 70,y\ge 14$ and $x-y\ge 5$
• D. $14x+5y\ge 70,y\ge 14$ and $x-y\le 5$
• E. $14x+5y\ge 70,y\le 14$ and $x-y\le 5$

Answer 1

Answer: (E)

$14x+5y\ge 70,y\le 14$ and $x-y\le 5$

Equation of line joining $(5,0)$ and $(0,14)$ is $y-0=\frac{14-0}{0-5}(x-5)$

$\Rightarrow -5y=14x-70\Rightarrow 14x+5y=70$

The shaded region is above the line.

Therefore, $14x+5y\ge 70$

Equation of line joining $(5,0)$ and $(19,14)$ is $y-0=\frac{14-0}{19-5}(x-5)$

$\Rightarrow y=x-5\Rightarrow x-y=5$

The shaded region is bounded by the line.

Thus $x-y\le 5$

Equation of line joining $(0,14)$ and $(19,14)$ is $y=14$

Shaded region is below the lines.

Therefore, $y\le 14$

So, option E is correct.