Question 84763This question is from textbook finite mathmatics
: Select the point which is in the feasible region
of the system of inequalities.
2x + 3y < 8
5x + 2y < 7
x > 0, y > 0
A. (1,2)
B. (1,1)
C. (0,3)
D. (3,2)
This question is from textbook finite mathmatics
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website!
Select the point which is in the feasible region
of the system of inequalities.
2x + 3y < 8
5x + 2y < 7
x > 0, y > 0
A. (1,2)
B. (1,1)
C. (0,3)
D. (3,2)
Substitute each of these points in each of the inequalities
to fnd out which one(s) satisies them all:
Try A:
Substituting (x,y) = (1,2) in the first inequality:
2x + 3y < 8
2(1) + 3(2) < 8
2 + 6 < 8
8 < 8
That is true. So we substitute it in the second inequality:
5x + 2y < 7
5(1) + 2(2) < 7
5 + 4 < 7
9 < 7
That is false, so we know (1,2) is not in the feasible region,
and (A) is not a correct choice.
-----------------------------------------
Try B:
Substituting (x,y) = (1,1) in the first inequality:
2x + 3y < 8
2(1) + 3(1) < 8
2 + 3 < 8
5 < 8
That is true. So we substitute it in the second inequality:
5x + 2y < 7
5(1) + 2(1) < 7
5 + 2 < 7
7 < 7
That is also true. So we substitute it in the third inequality:
x > 0
1 > 0
That is also true. So we substitute it in the fourth inequality:
y > 0
1 > 0
That is also true, so (1,1) is in the feasible region. So
(B) is a correct choice.
------------------------------------
Let's see if it could be either of the other two:
Try C:
Substituting (x,y) = (0,3) in the first inequality:
2x + 3y < 8
2(0) + 3(3) < 8
0 + 9 < 8
9 < 8
That is false. So we have eliminated C.
---------------------------------------------
Try D:
Substituting (x,y) = (3,2) in the first inequality:
2x + 3y < 8
2(3) + 3(2) < 8
6 + 6 < 8
12 < 8
That is false. So we have eliminated D.
So the only correct choice is (B).
Edwin
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