Question

The maximum value of $Z=4x+y$ subject to the constraints, $x+y\le ,50,3x+y\le 90,x\ge 0,y\ge 0$ is

• A. 40
• B. 130
• C. 120
• D. 50

Answer 1

Answer: (C)

Given $LPP$, max $Z=4x+y$
Subject to, $x+y\le 50$
$3x+y\le 90$
$x\ge 0,y\ge 0$
By Graphical method
$\begin{array}{cc}Equations& points\\ x+y=500& \left(0,50\right),\left(50,0\right)\\ 3x+y=90& \left(0,90\right),\left(30,0\right)\end{array}$
Let $20$ unit $=1sq$

Convex polygon is $OABC$
By corner Point Method,
$A(30,0)4.30+1.0=120$
$B(0,50)4.0+1.50=50$
$C(20,30)4.20+1.30=110$
Hence, maximum value of $z=120$