Graph the following system of inequalities. Show (by shading in) the feasible region. x + 2 y ≤ 12 2 x + y ≤ 12 x ≥ 0 , y ≥ 0

Question

Graph the following system of inequalities. Show (by shading in) the feasible region.  x  +  2  y  ≤  12  2  x  +  y  ≤  12  x  ≥  0  ,  y  ≥  0

szilincsifs · Accepted Answer

To graph such an inequality, start by graphing the boundary.For example, the boundary of   x  +  2  y  ≤  12, is the line   x  +  2  y  =  12. To graph a line, you only need two points. If x= 0, that equation becomes 2y= 12 so y= 6. Mark (0, 6) on the graph. If y= 0, that equation becomes x= 12 so mark (12, 0) on the graph. Draw the line through those two points.That line, where x+ 2y= 12, separates   x  +  2  y  &amp;lt;  12 from   x  +  2  y  &amp;gt;  12. It is easy to see that (0, 0) satisfies   0  +  2  (  0  )  =  0  &amp;lt;  12 so every point on the same side of that line as (0, 0) satisfies this inequality. Do the same for each of the other inequalities.The &quot;feasible region&quot;, the region where all of these inequalities are satisfied, is where those all overlap- their &quot;intersection&quot;.

Graph the following system of inequalities. Show (by shading in) the feasible region. x + 2

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