Mathematics - Area Under Curves Question with Solution | TestHub

$3x+5y=\mathrm{26....}\left(i\right)\times 5$
$5x+3y=\mathrm{30....}\left(ii\right)\times 3$
$15x+25y=130$
$15x+9y=90$
$16y=40$
$y=\frac{40}{16}=\frac{5}{2}$
$\therefore 3x+\frac{5\times 5}{2}=26$
$3x=26-\frac{25}{2}$
$x=\frac{9}{2}$
$z=2x+y$
Now check values of objective function at corner points of the shaded region
$Z_A=2\times 6+0=12$
$Z_B=2\times \frac{9}{2}+\frac{5}{2}=9+2.5=11.5$
$Z_C=2\times 0+\frac{26}{5}=\frac{26}{5}=5.2$
Hence$Z_{\max }=12$at$x=6$and$y=0$