9. A vertex of a feasible region by the linear constraints 2x + y greater than equal to 30, x + 2y is greater than equal to 24 and x, y is small than equal to 0 is (a) (0,10) (b) (12,6) (d) (14,0) (c) (0,2)
Answers
Answer:
A vertex of a feasible region by the linear constraints 2x + y greater than equal to 30, x + 2y is greater than equal to 24 and x, y is small than equal to 0 is (a) (0,10) (b) (12,6) (d) (14,0) (c) (0,2)
The correct option is (b).
Given:
2x + y ≥ 30
x + 2y ≥ 24
x ≥ 0, y ≥ 0
To find: a possible vertex of the feasible region
Solution:
Required point is a vertex
⇒ Required point is a part of feasible region and satisfies all inequalities.
We have four options - (0,10), (12,6), (14,0), (0,2).
Taking inequality 1, we get
2(0) + 10 = 10 < 30 ⇒ (0, 10) is rejected
2(12) + 6 = 30 ≥ 30 ⇒ (12, 6) is selected
2(14) + 0 = 28 < 30 ⇒ (14, 0) is rejected
2(0) + 2 = 2 < 30 ⇒ (0, 2) is rejected
Now, we shall see if the point (12, 6) satisfies the remaining inequalities
12 + 2(6) = 24 ≥ 24 ⇒ satisfied
12 ≥ 0 ⇒ satisfied
6 ≥ 0 ⇒ satisfied
⇒ (12, 6) is the only point that fulfils all inequalities
⇒ It is the only point that can be a vertex
∴ The correct option is (b)
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