Question

Maximum value of $Z=3x+4y$ subject to constraints $x-y\le -1$, $-x+y\le 0$ and $x,y\ge 0$, is given by

• A. $1$
• B. $4$
• C. $6$
• D. No Feasible Region

Answer 1

The correct option is D

No Feasible Region

Explaination for the correct option:

Finding the maximum value:

Given $Z=3x+4y$

The given constraints are $x-y\le -1,-x+y\le 0$ and $x,y\ge 0$

Let us consider the equations as

$$\begin{gathered} x-y=-1 \\ -x+y=0 \end{gathered}$$

Adding both equations, we get

$$\begin{gathered} x-y-x+y=-1+0 \\ \Rightarrow 0=-1 \end{gathered}$$

which is wrong.

Also on plotting the graph of the constraint inequalities we get

There is no common point or commonly feasible area and thus there will be no maximum value.

Hence, option (4) is correct.