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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The maximum value of $z=4x+2y$ subject to constraints
$2x+3y \le 28$,
$x+y \le 10$,
$x,y \ge 0$ is:
Solution
Corner points of feasible region:
$(0,0)$
From $x+y=10$
If $x=0$, $y=10$ → but check first constraint:
$2(0)+3(10)=30>28$ ❌ not feasible
So take intersection of
$2x+3y=28$
$x+y=10$
Solve:
$y=10-x$
Substitute:
$2x+3(10-x)=28$
$2x+30-3x=28$
$-x=-2$
$x=2$
Then
$y=10-2=8$
So intersection point $(2,8)$
Now check intercepts:
If $y=0$
From $x+y=10$ → $x=10$
Check first constraint:
$2(10)+0=20\le 28$ ✔
So point $(10,0)$ is feasible.
Now evaluate $z=4x+2y$
At $(0,0)$ → $0$
At $(2,8)$ → $4(2)+2(8)=8+16=24$
At $(10,0)$ → $40$
Maximum value = 40
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