UGC NET Computer Science Linear Programming Previous Year Questions (PYQs)

Stock available:

Red wool = $8$

Green wool = $10$

Blue wool = $15$

Dual objective function uses resource quantities.

Thus

$Min\ P = 8u + 10v + 15w$

Let

$x$ = unit of cloth A

$y$ = unit of cloth B

Income:

$Max\ Z = 30x + 50y$

Constraints

$2x + 3y \le 8$

$3x + 2y \le 10$

$2y \le 15$

Corner point:

$x = 0.8,\ y = 2$

$Z = 30(0.8) + 50(2)$

$Z = 24 + 100$

$Z = 124$

Red wool constraint

$2x + 3y \le 8$

Green wool constraint

$3x + 2y \le 10$

Blue wool constraint

$2y \le 15$

or

$y \le 7.5$

At optimal point

$2x + 3y = 8$

$3x + 2y = 10$

Solve

$x = 0.8$

Income per unit cloth

A = ₹30

B = ₹50

Thus objective function

$Max\ Z = 30x + 50y$