The shaded region in the figure is the solution set of the inequations

• A

  \( 5 x+4 y \geq 20, x \leq 6, y \geq 3, x \geq 0, y \geq 0 \)
• B

  \( 5 x+4 y \leq 20, x \leq 6, y \leq 3, x \geq 0, y \geq 0 \)
• Correct answer
  C

  \( 5 x+4 y \geq 20, x \leq 6, y \leq 3, x \geq 0, y \geq 0 \)
• D

  \( 5 x+4 y \geq 20, x \geq 6, y \geq 3, x \geq 0, y \geq 0 \)

Solution

From given shaded region we have

\[ \begin{array}{l} 6 \geq x \geq 0,3 \geq y \geq 0 \\ y \geq-\frac{5}{4} x+5 \\ \Rightarrow 5 x+4 y \geq 20 \end{array} \]

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