The maximum value of the objective function $Z=2x+y$ of an LPP, subject to the constraints $x ≤6,y≤ 2, x-y≤0, x≥0, y ≥0$, is

6

The correct answer is Option (2) → 6

$Z=2x+y$

Constraints:

$x\le 6,\; y\le 2,\; x-y\le 0,\; x\ge 0,\; y\ge 0$

The condition $x-y\le 0$ gives $x\le y$.

Since $y\le 2$, the largest possible $x$ satisfying $x\le y$ is $x=2$.

Thus the feasible point giving maximum value is:

$x=2,\; y=2$

Evaluate $Z$:

$Z=2(2)+2=6$

The maximum value of $Z$ is $6$.