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:
Answer & explanation
Correct answer: option 3
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.