Corner points of the feasible region for an LPP are $(0,2),(3,0),(6,0),(6,8)$ and $(0,5)$. Let $Z=4 x+6 y$ be the objective function. The minimum value of $z$ occurs at

• A

  Only $(0,2)$
• B

  Only $(3,0)$
• C

  The mid-point of the line segment joining the points $(0,2)$ and $(3,0)$
• Correct answer
  D

  Any point on the line segment joining the points $(0,2)$ and $(3,0)$

Solution

$\therefore$ Minimum of $Z$ occur at $(0,2)$ and $(3,0)$. $\therefore$ Minimum value of $Z$ occur at any point on the line segment $(0,2)$ and $(3,0)$.

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