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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Consider the following linear optimization problem:
Maximize $Z=6x+5y$
Subject to $2x-3y\le 5$
$x+3y\le 11$
$4x+y\le 15$
and $x\ge 0,\ y\ge 0$.
The optimal solution of the problem is:
Maximize $Z=6x+5y$
Subject to $2x-3y\le 5$
$x+3y\le 11$
$4x+y\le 15$
and $x\ge 0,\ y\ge 0$.
The optimal solution of the problem is:
Solution
Check corner points of feasible region.Intersection of $x+3y=11$ and $4x+y=15$:
From $4x+y=15$,
$y=15-4x$
Put in $x+3y=11$:
$x+3(15-4x)=11$
$x+45-12x=11$
$-11x=-34$
$x=\frac{34}{11}$
Now,
$y=15-4\cdot\frac{34}{11}=\frac{29}{11}$
Objective value:
$Z=6x+5y$
$Z=6\cdot\frac{34}{11}+5\cdot\frac{29}{11}$
$Z=\frac{204+145}{11}=\frac{349}{11}=31.72$
Other corner values are smaller.
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