For the following shaded area, the linear constraints except x ≥ 0 and y ≥ 0 , are

Question

For the following shaded area, the linear constraints except x ≥ 0 and y ≥ 0 , are (A) 2x + y ≤ 2 , x - y ≤ 1, x + 2y ≤ 8  (B) 2x + y ≥ 2 , x - y ≤ 1, x + 2y ≤ 8  (C) 2x + y ≥ 2 , x - y ≥ 1, x + 2y ≤ 8  (D) 2x + y ≥ 2 , x - y ≥ 1, x + 2y ≥ 8

Tardigrade Admin · Accepted Answer

To test the origin for 2x + y = 2 ,x - y = 1 and x + 2y = 8 in reference to shaded area, 0 + 0 < 2 is true for 2x + y = 2 . So for the region does not include origin (0, 0), 2x + y ≥ 2. Again for x - y = 1, 0 - 0 < 1, ∴ x - y ≤ 1 Similarly for x + 2y = 8, 0 + 0 < 8: ∴ x + 2y ≤ 8 .

Q. For the following shaded area, the linear constraints except $x \geq 0$ and $y \geq 0$ , are

$2 x + y \leq 2, x - y \leq 1, x + 2 y \leq 8$

$2 x + y \geq 2, x - y \leq 1, x + 2 y \leq 8$

$2 x + y \geq 2, x - y \geq 1, x + 2 y \leq 8$

$2 x + y \geq 2, x - y \geq 1, x + 2 y \geq 8$

Q. For the following shaded area, the linear constraints except x≥0 and y≥0 , are

2x+y≤2,x−y≤1,x+2y≤8

2x+y≥2,x−y≤1,x+2y≤8

2x+y≥2,x−y≥1,x+2y≤8

2x+y≥2,x−y≥1,x+2y≥8

To test the origin for 2x+y=2,x−y=1 and x+2y=8 in reference to shaded area,0+0<2 is true for 2x+y=2 . So for the region does not include origin (0, 0), 2x+y≥2. Again for x−y=1,0−0<1,∴x−y≤1 Similarly for x+2y=8,0+0<8:∴x+2y≤8.

Q. For the following shaded area, the linear constraints except $x \geq 0$ and $y \geq 0$ , are

$2 x + y \leq 2, x - y \leq 1, x + 2 y \leq 8$

$2 x + y \geq 2, x - y \leq 1, x + 2 y \leq 8$

$2 x + y \geq 2, x - y \geq 1, x + 2 y \leq 8$

$2 x + y \geq 2, x - y \geq 1, x + 2 y \geq 8$