The feasible region for an LPP is shown in the figure given below. If objective is maximizing $Z=22x+18y $ find (x, y) for the optimal Z.

(8, 12)

Corner points from the figure

$O(0,0)$

$B(0,20)$

$D(16,0)$

$P$ = intersection of $x+y=20$ and $3x+2y=48$

Find point $P$

$x+y=20$

$3x+2y=48$

$y=20-x$

$3x+2(20-x)=48$

$3x+40-2x=48$

$x=8$

$y=12$

$P(8,12)$

Evaluate $Z=22x+18y$

$Z(0,0)=0$

$Z(0,20)=360$

$Z(16,0)=352$

$Z(8,12)=22(8)+18(12)=176+216=392$

Maximum value occurs at $(8,12)$.