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प्रश्न
A manufacturer of electronic circuits has a stock of 200 resistors, 120 transistors and 150 capacitors and is required to produce two types of circuits A and B. Type A requires 20 resistors, 10 transistors and 10 capacitors. Type B requires 10 resistors, 20 transistors and 30 capacitors. If the profit on type A circuit is Rs 50 and that on type B circuit is Rs 60, formulate this problem as a LPP so that the manufacturer can maximise his profit.
उत्तर
Let x units of type A and y units of type B electric circuits be produced by the manufacturer.
As per the given information, we construct the following table:
| Items | Type A (x) | Type B (y) | Maximum stock |
| Resistors | 20 | 10 | 200 |
| Transistors | 10 | 20 | 120 |
| Capacitors | 10 | 30 | 150 |
| Profit | ₹ 50 | ₹ 60 | Z = 50x + 60y |
Now, we have the total profit in rupees Z = 50x + 60y to maximise subject to the constraints
20x + 10y ≤ 200 .....(i)
10x + 20y ≤ 120 ......(ii)
10x + 30y ≤ 150 ......(iii)
x ≥ 0, y ≥ 0 ......(iv)
Hence, the required LPP is
Maximise Z = 50x + 60y subject to the constraints
20x + 10y ≤ 200 ⇒ 2x + y ≤ 20
10x + 20y ≤ 120 ⇒ x + 2y ≤ 12
And 10x + 30y ≤ 150 ⇒ x + 3y ≤ 15, x ≥ 0, y ≥ 0
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