Aspire Faculty ID #18720 · Topic: UGC NET Computer Science Sep 2022 (Paper II) · Just now
UGC NET Computer Science Sep 2022 (Paper II)

Maximize $z=5x_1+12x_2+4x_3$

Subject to $x_1+2x_2+x_3=10$

$2x_1-x_2+3x_3=8$

$x_1,x_2,x_3\ge 0$

its dual problem is

Minimize $w=10y_1+8y_2$

Subject to $y_1+2y_2\ge 5$

$2y_1-y_2\ge 12$

$y_1+3y_2\ge 4$

Which of the following is correct?

Solution

In primal maximization problem,

If the constraint is equality type, then the corresponding dual variable is unrestricted.

Here, first constraint is equality type, so

$y_1$ is unrestricted.

The expected condition for second dual variable is

$y_2\ge 0$

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