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Question
Refer to quastion 12. What will be the minimum cost?
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Solution
As per the solution of Question No.12
We have Z = 400x + 200y
Subject to the constraints
5x + 2y ≥ 30 ......(i)
2x + y ≤ 15 ......(ii)
x ≤ y, x ≥ 0, y ≥ 0
x – y ≤ 0 .....(iii)
Let 5x + 2y = 30
| x | 0 | 6 |
| y | 15 | 0 |
Let 2x + y = 15
| x | 0 | 7.5 |
| y | 15 | 0 |
Let x – y = 0
| x | 0 | 1 |
| y | 0 | 1 |
Solving equation (i) and (iii) we get
x = `30/7` and y = `30/7`
And on solving equation (ii) and (iii) we get, x = 5 and y = 5
Here, ABC is the shaded feasible region whose corner points are `"A"(30/7, 30/7)`, B(5, 5) and C(0, 15)
Evaluating the value of Z, we have
| Corner points | Value of Z = 400x + 200y | |
| `"A"(30/7, 30/7)` |
Z = `400(30/7) + 200(30/7)` = `18000/7` = 2571.4 |
← Minimum |
| B(5, 5) | Z = 400(5) + 200(5) = 3000 | |
| C(0, 15) | Z = 400(0) + 200(15) = 3000 |
Hence, the required minimum cost is ₹ 2571.4 at `(30/7, 30/7)`.
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