Question

For the following shaded region, the linear constraint are:

विकल्प

• x + 2y ≤ 6, 5x + 3y ≤ 15, x ≤ 7, y ≤ 6, x, y ≥ 0

• x + 2y ≥ 6, 5x + 3y ≥ 15, x ≤ 7, y ≤ 6, x, y ≥ 0

• x + 2y ≤ 6, 5x + 3y ≥ 15, x ≤ 7, y ≤ 6, x, y ≥ 0

• x + 2y ≥ 6, 5x + 3y ≤ 15, x ≤ 7, y ≤ 6, x, y ≥ 0

Answer 1

x + 2y ≥ 6, 5x + 3y ≥ 15, x ≤ 7, y ≤ 6, x, y ≥ 0

Explanation:

From the line x + 2y = 6, shaded region is away from the origin

`\implies` x + 2y ≥ 6

From the line 5x + 3 y = 15, shaded region is away from the origin

`\implies` 5x + 3y ≥ 15

From the line x = 7, shaded region is towards the origin

`\implies` x ≤ 7

From the line y = 6, shaded region is towards the origin

`\implies` y ≤ 6

∵ Shaded region is in the first quadrant `\implies` x, y ≥ 0