The optimal solution of the L.P.P. Maximize : $\mathrm{Z}=8 x+3$ y subject to the constraints $x+y \leq 3,4…
The optimal solution of the L.P.P. Maximize : $\mathrm{Z}=8 x+3$ y subject to the constraints $x+y \leq 3,4 x+y \leq 6, x \geq 0, y \geq 0$ is
$x=0, y=3$
$x=0, y=0$
$x=\frac{3}{2}, y=0$
$x=1, y=2$
Solution
Here $\mathrm{O} \equiv(0,0), \mathrm{A} \equiv\left(\frac{3}{2}, 0\right), \mathrm{C}=(0,3)$
Point of intersection of given lines is $\mathrm{B} \equiv(1,2)$
$Z=8 x+3 y$ and feasible region is shaded.
$Z_{(0)}=0$
$Z_{(A)}=8\left(\frac{3}{2}\right)=12$
$Z_{(C)}=3(3)=9$
$Z_{(B)}=8(1)+3(2)=14$
