Question

The minimum value of $z=2x_1+3x_2$ subject to the constraints $2x_1+7x_2\ge 22$ , $x_1+x_2\ge 6,5x_1+x_2\ge 10$ and $x_1,x_2\ge 0$ is

• A. 14
• B. 20
• C. 10
• D. 16

Answer 1

Answer: (A)

We have, $z=2x_1+3x_2$ Subject to the constraints
$2x_1+7x_2\ge 22$
$x_1+x_2\ge 6$
$5x_1+x_2\ge 10$
$x_1,x_2\ge 0$
The graph of inequalities are

The feasible region are $ABCD$

Corner points		$X=2x_1+3x_2$
A	A (11, 0)	i	22 + 0 = 22
B	B(4, 2 )	ii	8 + 6 = 14
C	C(1, 5)	iii	2 + 15 = 17
D	D ( 0, 10)	iv	0 + 30 = 30

Minimum value of $Z$ ia $14$