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  • Show that the solution set of the following system of linear inequalities is an unbounded region 2x+y>8, x+2y>10, x>0,y>0

Q: Show that the solution set of the following system of linear inequalities is an unbounded region  2x+y \geq 8, x+2y\geq 10, x\geq 0, y\geq 0

Answers (1)

Let us find the common region of all by plotting each inequality.

2x + y ≥ 8  …… (given)

Thus, for line,

2x + y = 8

x          

0          

8            

y

4

0

Now, we know that (0,0) does not satisfy 2x + y ≥ 8

Thus, The region is away from the origin.

Now, x + 2y ≥ 10 …… (given)

Thus, for line,

x + 2y = 10

x      

0         

8     

y

5

0

Now, we know that (0,0) does not satisfy x + 2y ≥ 10

Thus, The region is away from the origin.

Also, x ≥ 0 & y ≥ 0 implies that the region is in the first quadrant

Thus, the graph will be -

Hence, from the graph it is clear that the shaded region is unbounded.

 

Posted by

infoexpert22

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