The vertices of the feasible region for the constraints $x+y \leq 4, x \leq 2, y \leq 1, x+y \geq 1, x$, $y \geq 0$ are

• A

  (1,0),(2,0),(2,1),(0,4)
• B

  (0,1),(4,0),(0,4),(1,0)
• Correct answer
  C

  (1,0),(2,0),(2,1),(0,1)
• D

  (1,0),(4,0),(2,1),(0,4)

Solution

Feasible region lies on origin side of $x+y=4$, $x=2, y=1$ and non-origin side of $x+y=1$ and in first quadrant. $\therefore \quad$ Vertices of feasible region are $\mathrm{A}(1,0), \mathrm{B}(2,0), \mathrm{C}(2,1), \mathrm{D}(0,1)$

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