Question

Determine the system of linear equation for which the solution set is the shaded region in the following figure ______.

विकल्प

• x ≤ 5, y ≤ 4, x + y ≤ 6, 5x + 2y ≥ 10, y ≥ 0, x ≥ 0 

• x ≤ 5, y ≤ 4, x + y ≥ 6, 5x + 2y ≤ 10, y ≥ 0, x ≥ 0 

• x ≥ 5, y ≥ 4, x + y ≤ 6, 5x + 2y ≥ 10, y ≥ 0, x ≥ 0 

• x ≥ 5, y ≥ 4, x + y ≥ 6, 5x + 2y ≤ 10, y ≥ 0, x ≥ 0 

Answer 1

Determine the system of linear equation for which the solution set is the shaded region in the following figure x ≤ 5, y ≤ 4, x + y ≤ 6, 5x + 2y ≥ 10, y ≥ 0, x ≥ 0.

Explanation:

Take a test point (2, 2) that lies within the feasible region

Since (2) + (2) = 4 ≤ 6 is true, we have x + y ≤ 6

Since 5(2) + 2(2) = 14 ≥ 10, we have 5x + 12y ≥ 10.

Since 2 ≤ 5 and 2 ≤ 4 are true, we have x ≤ 5 and y ≤ 4.