Question

The maximum value of $z=4x+2y$ subject to constraints $2x+3y\le 18$ , $x+y\ge 10$ and $x,y\ge 0$ is

• A. $20$
• B. $36$
• C. $40$
• D. None of these

Answer 1

The correct option is D

None of these

Explanation for the correct option:

Find the critical points of the given function.

In the question, a function $z=4x+2y$ is given, and the constraints $2x+3y\le 18$, $x+y\ge 10$, and $x,y\ge 0$ is also given.

Draw a graph describing the given inequalities as follows:

From the graph, it is clear that there is no critical point. because there is no area in the graph where all the four given inequalities hold.

So, The given function $z=4x+2y$ does not attain any maximum value.

Hence, option $D$ is the correct answer.