Which one of the following inequalities is redundant for the shaded feasible region (ABCDA) shown below?

$4x + 3y ≤60$

The correct answer is Option (3) → $4x + 3y ≤60$

A redundant inequality is one that does not affect the feasible region because the region already satisfies it due to the other inequalities. 

The feasible region is already bounded by:

• x + 2y ≤ 40
• 3x + y ≥ 30
• x ≥ 0, y ≥ 0

The line 4x + 3y = 60 does not form any boundary segment of the shaded region. Even if this inequality is removed, the feasible region remains unchanged.

Hence, the inequality: 4x + 3y ≤ 60 is redundant.