Question

The maximum value of $P=x+3y$ such that $2x+y\le 20,x+2y\le 20,x\ge 0,y\ge 0,$ is.

• A. $50$
• B. $40$
• C. $30$
• D. None of these

Answer 1

The correct option is C $30$

The points in the feasible region are $A(0,0),B(0,10),C\left(\frac{20}{3},\frac{10}{3}\right)$ and $D(10,0)$.
Objective function is $(P=x+3y)$
At point A, $P=0+3\left(0\right)=0$
At point B, $P=0+3\left(10\right)=30$
At point C, $P=\frac{20}{3}+\frac{3\left(10\right)}{3}=\frac{50}{3}$
At point D, $P=10+3\left(0\right)=10$
$\therefore$ Maximum value of $P=30$ at $B(0,10)$.