Question

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

• A. $(0,2)$ only
• B. $(3,0)$ only
• C. the mid-point of the line segment joining the points $(0,2)$ and $(3,0)$ only
• D. any point on the line segment joining the points $(0,2)$ and $(3,0)$

Answer 1

The correct option is D any point on the line segment joining the points $(0,2)$ and $(3,0)$

$$\begin{array}{cc}\text{Corner Points}& Z=4x+6y\\ (0,2)& 4\times 0+6\times 2=12\\ (3,0)& 4\times 3+6\times 0=12\\ (6,0)& 4\times 6+6\times 0=24\\ (6,8)& 4\times 6+6\times 8=72\\ (0,5)& 4\times 0+6\times 5=30\end{array}$$Since the minimum value of $Z=12$ occurs at two distinct corner points, $(0,2)$ and $(3,0),$ it occurs at every points of the line segment joining these two points.