The shaded region shown in fig. is given by the inequation

• Correct answer
  A

  \( 14 x+5 y \geq 70 ; y \leq 14 \) and \( x-y \leq 5 \)
• B

  \( 14 x+5 y \geq 70 ; y \leq 14 \) and \( x-y \geq 5 \)
• C

  \( 14 x+5 y \leq 70 ; y \leq 14 \) and \( x-y \geq 5 \)
• D

  \( 14 x+5 y \geq 70 ; y \geq 14 \) and \( x-y \geq 5 \)

Solution

Let points, $A(0,14), B(5,0)$ and $C(19,14)$
Now, equation of side $\mathrm{AB}$ is $\frac{x}{5}+\frac{y}{14}=1$ $\Rightarrow 14 x+5 y=70 \rightarrow(1)$ Equation of side $\mathrm{AC}$ is $y=14 \rightarrow(2)$ and equation of side $\mathrm{BC}$ is $x-y=5 \rightarrow(3)$ Therefore, the shaded region shown in figure is given by the inequation $14 x+5 y>70 y < 14$ and $x-y < 5$

Hence, the correct answer is option: 'A'.