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

(40, 15)

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 $55$.