In number theory, it is often important to find factors of an integer N. The number N has two trivial factors, namely 1 and N. Any other factor, if…

In number theory, it is often important to find factors of an integer N. The number N has two trivial factors, namely $\displaystyle 1$ and N. Any other factor, if exists, is called non-trivial factor of N. Naresh has plotted a graph of some constraints (linear inequations) with points A $\displaystyle (0, 50)$, B $\displaystyle (20, 40)$, C $\displaystyle (50, 100)$, D $\displaystyle (0, 200)$ and E $\displaystyle (100, 0)$. This graph is constructed using three non-trivial constraints and two trivial constraints. One of the non-trivial constraints is $\displaystyle \mathrm{x}+2 \mathrm{y} \geq 100$.

Based on the above information, answer the following questions :

What are the two trivial constraints?

If $\displaystyle \mathrm{R}_1$ is the feasible region, then find the maximum value of the objective function $\displaystyle \mathrm{z}=5 \mathrm{x}+2 \mathrm{y}$.