1. Tardigrade
  2. Question
  3. Mathematics
  4. 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

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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

AMUAMU 2010Linear Programming

Solution:

Given $LPP$, max $Z = 4x + y$
Subject to, $x+y \le\,50 $
$3x+y \le\, 90$
$x \ge0, y \ge\,0$
By Graphical method
$\begin{matrix}Equations&points\\ x+y=500&\left(0,50\right), \left(50,0\right)\\ 3x+y=90&\left(0, 90\right), \left(30, 0\right)\end{matrix}$
Let $20$ unit $=1\,sq$
image
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 $z = 120$