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Question : 24
Total: 29
A small firm manufactures gold rings and chains. The total number of rings and chains manufactured per day is at most 24. It takes 1 hour to make a ring and 30 minutes to make a chain. The maximum number of hours available per day is 16. If the profit on a ring is Rs. 300 and that on a chain is Rs. 190, find the number of rings and chains that should be manufactured per day, so as to earn the maximum profit. Make it as an L.P.P. and solve it graphically.
Solution:
Let x be the number of gold rings and y be number of chains manufactured L.P.P. is
Max Z = 300x + 190y
Substitute in x + y ≤ 24
x +
x ≥ 0 , y ≥ 0
Feasible region
Hence to make the maximum profit, 8 gold rings and 16 chains must be manufactured.
Max Z = 300x + 190y
Substitute in x + y ≤ 24
x +
x ≥ 0 , y ≥ 0
Feasible region
| Corner Points | Value of Z = 300x + 190y | |
|---|---|---|
| A (0, 24) | 4560 | |
| B (8, 16) | 5440 | Maximum |
| C (16, 0) | 4800 | |
| O (0, 0) | 0 |
Hence to make the maximum profit, 8 gold rings and 16 chains must be manufactured.
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