Let the factory makes x pieces of item A and B by pieces of item.
Time required by item A (one piece)
cutting = 5 minutes, assembling = 10 minutes
Time required by item B (one piece)
cutting = 8 minutes, assembling = 8 minutes
Total time cutting = 3 hours & 20 minutes, assembling = 4 hours
Profit on one piece item A = Rs 5, item B = Rs 6
Thus, our problem is maximized Z = 5x + 6y
Subject to x ≥ 0, y ≥ 0
5x + 8y ≤ 200
10x + 8y ≤ 240
On plotting graph of above constraints or inequalities, we get shaded region.
From figure, possible points for maximum value of z are at (24, 0), (8, 20), (0, 25). at (24, 0), z = 120
at (8, 20), z = 40 + 120 = 160 (maximum)
at (0, 25), z = 150
∴ 8 pieces of item A and 20 pieces of item B produce maximum profit of Rs 160.