A publisher binds books in two editions. A batch of hardbacks needs 2 hours of binding and a batch of paperbacks needs 1 hour, and 90 hours of binding are available. The number of paperback batches must be at least the number of hardback batches. The profit is Rs. 60 on a batch of hardbacks and Rs. 25 on a batch of paperbacks. The maximum profit is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 2550
Let x batches of hardbacks and y batches of paperbacks be bound. Then
Maximise \(Z = 60x + 25y\)
subject to
\(2x + y \le 90\) (binding)
\(y \ge x\)
\(x \ge 0,\ y \ge 0\)
The line \(y = x\) meets \(2x + y = 90\) where \(3x = 90\), that is at (30, 30).
The corner points are (0, 0), (30, 30) and (0, 90). Values of Z:
\(Z(0, 0) = 0\)
\(Z(30, 30) = 1800 + 750 = 2550\)
\(Z(0, 90) = 2250\)
The maximum profit is Rs. 2550, with 30 batches of each edition.