A tailor has 48 m of cloth. A shirt needs 2 m of cloth and a kurta needs 3 m. The profit is Rs. 50 on a shirt and Rs. 80 on a kurta, and everything made is sold. The maximum profit the tailor can make from the cloth is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 1280
Let x shirts and y kurtas be made. Then
Maximise \(Z = 50x + 80y\)
subject to
\(2x + 3y \le 48\), \(x \ge 0\), \(y \ge 0\)
The feasible region is the triangle with corner points (0, 0), (24, 0) and (0, 16). Values of Z:
\(Z(0, 0) = 0\)
\(Z(24, 0) = 1200\)
\(Z(0, 16) = 1280\)
The maximum profit is Rs. 1280, by making 16 kurtas and no shirts.