Question

The shaded part of given figure indicates in feasible region, then the constraints are:

Options

• x, y ≥ 0, x + y ≥ 0, x ≥ 5, y ≤ 3

• x, y ≥ 0, x – y ≥ 0, x ≤ 5, y ≤ 3

• x, y ≥ 0, x – y ≥ 0, x ≤ 5, y ≥ 3

• x, y ≥ 0, x – y ≤ 0, x ≤ 5, y ≤ 3

Answer 1

x, y ≥ 0, x – y ≥ 0, x ≤ 5, y ≤ 3

Explanation:

In the given figure, OC line passes through (0, 0) and (3, 3).

So, the equation of a line is y = x.

Also, the shaded portion of this line is towards the X-axis, so x – y ≥ 0.

In the given figure, line AB is parallel to Y-axis.

∴ The equation of line AB is x = 5, also the shaded portion of this line is towards the origin, so x – 5 ≤ 0 or x ≤ 5.

In the given figure, line BC is parallel to X-axis.

Therefore, the equation of line BC is y = 3. Also, the shaded portion of this line is towards the origin, so y – 3 ≤ 0 or y ≤ 3.

Also, the shaded region lies in the first quadrant, so x ≥ 0 and y ≥ 0.

Hence, constraints of given shaded region are x, y ≥ 0, x – y ≥ 0, x ≤ 5, y ≤ 3.