Given: The objective function $Z=m x+n y$ has the same maximum value on the two corner points of the feasible region.
ion drawn with the feasible region shaded as,


- The corner points of the feasible region are:
C(15,15), B(5,5), M(10,0) \text { and } N(60,0)$
- There is no change in corner points occurs due to extra constraints.
$\begin{array}{|c|l|} \hline \text{Corner Points of feasible region} & z \\ \hline C(15,15) & 6 \\ \hline B(5,5) & 0 \\ \hline M(10,0) & 2 \\ \hline N(60,0) & 0 \\ \hline \end{array}$
- The maximum value of $x+3 y$ will occur at two points $C$ and $N$.
- Now check whether there is a possibility of multiple solutions.
- For that join the points $\mathrm{C}$ and $\mathrm{N}$. If the points $\mathrm{C}$ and $\mathrm{N}$ are lying at the same line segment $\mathrm{CN}$ so for all the points on that line segment $\mathrm{CN}$, the value of the objective function will be a maximum of 60 .
- Since corner points $\mathrm{C}$ and $\mathrm{N}$ are lying on the same line segment $\mathrm{CN}$ so, at every point on the line segment $\mathrm{CN}$, we will get the maximum value of the objective function.
- So, the correct answer is option 2.