A person can sell a maximum of 20 units of shirts and pants on which a profit of Rs. 40 is made on each shirt and a profit of Rs. 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) → Rs. 640
Let x shirts and y pants be sold. The LPP is:
Maximize \(Z = 40x + 30y\)
\(x + y \le 20,\quad x \ge 2,\quad y \ge 4x\)
(\(y \ge 0\) follows from \(y \ge 4x\) and \(x \ge 2\).) The feasible region is a triangle. Its corner points are where two boundary lines meet:
\(x = 2\) and \(y = 4x\): (2, 8)
\(x = 2\) and \(x + y = 20\): (2, 18)
\(y = 4x\) and \(x + y = 20\): \(5x = 20\), so (4, 16)
The region is bounded, so the maximum of Z occurs at a corner point:
\(Z(2, 8) = 80 + 240 = 320\)
\(Z(2, 18) = 80 + 540 = 620\)
\(Z(4, 16) = 160 + 480 = 640\)
The maximum profit is Rs. 640, with 4 shirts and 16 pants.