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.
Answer & explanation
Correct answer: option 3
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 $(8,12)$.