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

$20$

Explanation for the correct option.

Given, $5x+4y\ge 2,x\le 6,y\le 7$, $z=x+2y$.

$\begin{array}{rcl}& \Rightarrow & 5x+4y=2\\ \frac{x}{{\displaystyle \frac{2}{5}}}+\frac{x}{{\displaystyle \frac{1}{2}}}& =& 1\end{array}$

Now, we have points $\left(\frac{2}{5},0\right),\left(0,\frac{1}{2}\right),x\le 6,y\le 7$ and check the maximum value of the function $z=x+2y$.

At point $A\left(\frac{2}{5},0\right),z=\frac{2}{5}$.

At point $B\left(6.0\right),z=6$.

At point $C(6,7),z=20$.

At point $D(0,7),z=14$.

At point $E\left(0,\frac{1}{2}\right),z=1$.

Therefore, the maximum value of the function $z=x+2y$ is $20$.

Hence, the correct option is D.