A manufacturer produces two products A and B. Both the products are processed on two different machines. The available capacity of the first machine is 12 hours and that of the second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on the first machine and 1 hour on the second machine. Each unit of product A is sold at Rs. 7 profit and that of B at a profit of Rs. 4. Find the production level per day for maximum profit graphically.
Answer: Max profit = Rs 26 at (2, 3): 2 units of A and 3 units of B
Solution
Let x units of A and y units of B be produced per day. Profit: Z=7x+4y. First machine: 3x+2y≤12 Second machine: 3x+y≤9 x≥0,y≥0 Corner points: (0,0), (3,0), (2,3) (intersection of 3x+2y=12 and 3x+y=9) and (0,6). Evaluate Z=7x+4y: (3,0): Z=21 (2,3): Z=14+12=26 ← maximum (0,6): Z=24
∴Zmax=Rs 26 at (2,3)
2 units of product A and 3 units of product B should be produced.Feasible region for 3x + 2y = 12 and 3x + y = 9, with corner points O(0, 0), A(3, 0), B(2, 3) and C(0, 6).
