Let $\mathbb{R}$ denote the set of all real numbers. Then the area of the region $\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: x>0, y>\frac{1}{x}, 5 x-4 y-1>0,4 x+4 y-17 <0\right\}$ is

• A

  $\frac{17}{16}-\log _e 4$
• Correct answer
  B

  $\frac{33}{8}-\log _e 4$
• C

  $\frac{57}{8}-\log _e 4$
• D

  $\frac{17}{2}-\log _e 4$

Solution

Area $=\frac{13}{8}+\frac{20}{8}-\log _e 4=\left(\frac{33}{8}-\log _e 4\right)$

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