Aspire Faculty ID #18840 · Topic: UGC NET Computer Science Nov 2021 (Paper II) · Just now
UGC NET Computer Science Nov 2021 (Paper II)

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:

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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