Consider the LPP: Maximize $Z = x + y$ subject to the constraints $x + 2y ≤ 70,2x + y ≤ 95, x, y ≥0$. The optimal feasible solution is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (40, 15)
Given LPP
Maximize $Z=x+y$
Subject to
$x+2y\le70$
$2x+y\le95$
$x\ge0,\;y\ge0$
Feasible corner points
$(0,0),\;(0,35),\;(40,15),\;\left(\frac{95}{2},0\right)$
Evaluate $Z$
$Z(0,0)=0$
$Z(0,35)=35$
$Z(40,15)=55$
$Z\left(\frac{95}{2},0\right)=\frac{95}{2}=47.5$
Maximum value is $55$ at $(40,15)$
The optimal feasible solution is $(40,15)$ and the maximum value of $Z$ is $55$.