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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Consider the following linear programming $(LP)$:
Maximize $z=2x_1+3x_2$
Such that
$2x_1+x_2\le 4$
$x_1+2x_2\le 5$
$x_1,x_2\ge 0$
The optimum value of the LP is
Maximize $z=2x_1+3x_2$
Such that
$2x_1+x_2\le 4$
$x_1+2x_2\le 5$
$x_1,x_2\ge 0$
The optimum value of the LP is
Solution
Corner points are checked for maximum value.At $(0,0)$:
$z=2(0)+3(0)=0$
At $(2,0)$:
$z=2(2)+3(0)=4$
At $(0,2.5)$:
$z=2(0)+3(2.5)=7.5$
Now solve intersection:
$2x_1+x_2=4$
$x_1+2x_2=5$
From first equation,
$x_2=4-2x_1$
Put in second equation:
$x_1+2(4-2x_1)=5$
$x_1+8-4x_1=5$
$-3x_1=-3$
$x_1=1$
Then,
$x_2=4-2(1)=2$
At $(1,2)$:
$z=2(1)+3(2)=2+6=8$
Maximum value is $8$.
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