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
Answer & explanation
Correct answer: option 2
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 $6$.