The maximum value of the objective function $Z = 8x + 2y$ of an L.P.P. subject to constraints $2x + y ≤3,2x+3y≤6,x≥0, y ≥ 0$ is:

12

The correct answer is Option (1) → 12

$\text{Objective: }Z=8x+2y$

$\text{Constraints: }2x+y\le 3,\;2x+3y\le 6,\;x\ge0,\;y\ge0$

$\text{Corner points: }(0,0),\;(0,2),\;(0.75,1.5),\;(1.5,0)$

$Z(0,0)=0$

$Z(0,2)=4$

$Z\left(\frac{3}{4},\frac{3}{2}\right)=8\cdot\frac{3}{4}+2\cdot\frac{3}{2}=6+3=9$

$Z(1.5,0)=12$

The maximum value of $Z$ is $12$.