Question

For the feasible region shown below, the non-trivial constraints of the linear programming problem are:

Options

• x + y ≤ 5, x + 3y ≤ 9 

• x + y ≤ 5, x + 3y ≥ 9 

• x + y ≥ 5, x + 3y ≤ 9 

• x + y ≥ 5, 3x + y ≤ 9 

Answer 1

x + y ≥ 5, x + 3y ≤ 9 

Explanation:

The two sloping lines are x + y = 5 (intercepts (0, 5), (5, 0)) and x + 3y = 9 (intercepts (0, 3), (9, 0)); they meet at (3, 2). The shaded strip is the region above x + y = 5 and below x + 3y = 9 (together with x, y ≥ 0), so the non‑trivial constraints are x + y ≥ 5 and x + 3y ≤ 9.