The region of the XOY-plane represented by
the inequalities
x 26, y 22, 2x + y s 10 is
(a) unbounded (b) a polygon
(c) exterior of a triangle (d) none of these.
Answers
Given : The region of the XOY-plane represented by the inequalities
x ≥ 6, y ≥ 2, 2x + y ≤ 10
To Find : Correct option :
(a) unbounded
(b) a polygon
(c) exterior of a triangle
(d) none of these.
Solution:
x ≥ 6,
y ≥ 2,
2x + y ≤ 10
y ≥ 2
=> y = 2 + k where k ≥ 0
2x + y ≤ 10
=> 2x + 2 + k ≤ 10
=> 2x + k ≤ 10
=> 2x ≤ 10 as k ≥ 0
=> x ≤ 5
but x ≥ 6
Hence there is no bounded region
Hence The region of the XOY-plane represented by the inequalities is unbounded
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Answer:
x ≥ 6,
y ≥ 2,
2x + y ≤ 10
y ≥ 2
=> y = 2 + k where k ≥ 0
2x + y ≤ 10
=> 2x + 2 + k ≤ 10
=> 2x + k ≤ 10
=> 2x ≤ 10 as k ≥ 0
=> x ≤ 5
but x ≥ 6
Hence there is no bounded region
Hence The region of the XOY-plane represented by the inequalities is unbounded
Step-by-step explanation: