Question

If given constraints are $5x+4y\ge 2,x\le 6,y\le 7$, then the maximum value of the function $z=x+2y$ is

• A. $13$
• B. $14$
• C. $15$
• D. $20$

Answer 1

The correct option is D $20$

Given,
$z=x+2y$
and $5x+4y=2$
$\Rightarrow \frac{x}{\frac{2}{5}}+\frac{y}{\frac{1}{2}}=1$
At point $A(\frac{2}{5},0),z=\frac{2}{5}+0=\frac{2}{5}$
At point $B(6,0),z=6+0=6$
At point $C(6,7),z=6+14=20$
At point $D(0,7),z=0+2\left(7\right)=14$
At point $E(0,\frac{1}{2}),z=0+2\left(\frac{1}{2}\right)=1$
$\therefore$ The maximum value of $z$ is $20$.