A person can sell a maximum of 20 units of shirts and pants on which a profit of ₹40 is made on each shirt and a profit of ₹30 on each pant. A minimum of 2 shirts are being sold, while pants are sold at least 4 times as many as shirts. Then the maximum profit is:

₹640

The correct answer is Option (3) → ₹640

Let number of shirts sold = $x$ and number of pants sold = $y$.

Constraints:

1. $x + y \leq 20$   (maximum of 20 units sold)

2. $x \geq 2$   (minimum of 2 shirts)

3. $y \geq 4x$   (pants sold at least 4 times the shirts)

Objective: Maximize profit $Z = 40x + 30y$

Substitute $y = 4x$ in $x + y \leq 20$:

$x + 4x \leq 20 \Rightarrow 5x \leq 20 \Rightarrow x \leq 4$

Also, $x \geq 2 \Rightarrow x = 2, 3, 4$ are feasible integer values.

Try all feasible values:

For $x = 2 \Rightarrow y = 8 \Rightarrow Z = 40(2) + 30(8) = 80 + 240 = 320$

For $x = 3 \Rightarrow y = 12 \Rightarrow Z = 40(3) + 30(12) = 120 + 360 = 480$

For $x = 4 \Rightarrow y = 16 \Rightarrow Z = 40(4) + 30(16) = 160 + 480 = 640$

Maximum Profit = ₹640 when 4 shirts and 16 pants are sold.