<PRE><B>Question 84763</B>
&lt;pre&gt;&lt;b&gt;&lt;font size = 4&gt;
Select the point which is in the feasible region
of the system of inequalities. 

2x + 3y &lt;u&gt;&lt;&lt;/u&gt; 8
5x + 2y &lt;u&gt;&lt;&lt;/u&gt; 7
x &lt;u&gt;&gt;&lt;/u&gt; 0, y &lt;u&gt;&gt;&lt;/u&gt; 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 &lt;u&gt;&lt;&lt;/u&gt; 8

2(1) + 3(2) &lt;u&gt;&lt;&lt;/u&gt; 8
     2 + 6 &lt;u&gt;&lt;&lt;/u&gt; 8
         8 &lt;u&gt;&lt;&lt;/u&gt; 8
That is true.  So we substitute it in the second inequality:

5x + 2y &lt;u&gt;&lt;&lt;/u&gt; 7
5(1) + 2(2) &lt;u&gt;&lt;&lt;/u&gt; 7
 5 + 4 &lt;u&gt;&lt;&lt;/u&gt; 7
     9 &lt;u&gt;&lt;&lt;/u&gt; 7

That is false, so we know (1,2) is not in the feasible region,
and (A) is not a correct choice.

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Try B:
Substituting (x,y) = (1,1) in the first inequality:

2x + 3y &lt;u&gt;&lt;&lt;/u&gt; 8

2(1) + 3(1) &lt;u&gt;&lt;&lt;/u&gt; 8
     2 + 3 &lt;u&gt;&lt;&lt;/u&gt; 8
         5 &lt;u&gt;&lt;&lt;/u&gt; 8
That is true.  So we substitute it in the second inequality:

5x + 2y &lt;u&gt;&lt;&lt;/u&gt; 7
5(1) + 2(1) &lt;u&gt;&lt;&lt;/u&gt; 7
 5 + 2 &lt;u&gt;&lt;&lt;/u&gt; 7
     7 &lt;u&gt;&lt;&lt;/u&gt; 7

That is also true. So we substitute it in the third inequality:

x &lt;u&gt;&gt;&lt;/u&gt; 0

1 &lt;u&gt;&gt;&lt;/u&gt; 0

That is also true. So we substitute it in the fourth inequality:

y &lt;u&gt;&gt;&lt;/u&gt; 0

1 &lt;u&gt;&gt;&lt;/u&gt; 0

That is also true, so (1,1) is in the feasible region. So
(B) is a correct choice.

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Let&#39;s see if it could be either of the other two:

Try C:
Substituting (x,y) = (0,3) in the first inequality:

2x + 3y &lt;u&gt;&lt;&lt;/u&gt; 8

2(0) + 3(3) &lt;u&gt;&lt;&lt;/u&gt; 8
     0 + 9 &lt;u&gt;&lt;&lt;/u&gt; 8
         9 &lt;u&gt;&lt;&lt;/u&gt; 8

That is false.  So we have eliminated C.

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Try D:
Substituting (x,y) = (3,2) in the first inequality:

2x + 3y &lt;u&gt;&lt;&lt;/u&gt; 8

2(3) + 3(2) &lt;u&gt;&lt;&lt;/u&gt; 8
     6 + 6 &lt;u&gt;&lt;&lt;/u&gt; 8
        12 &lt;u&gt;&lt;&lt;/u&gt; 8

That is false.  So we have eliminated D.

So the only correct choice is (B).

Edwin&lt;/pre&gt;</PRE>