Question 1040255
.
x>0
y>0. 
3x+2y>18
6x+7y<42
What is the value of 3x+3y
Thank you
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<TABLE> 
  <TR>
  <TD> 

{{{graph( 330, 330, -10.5, 10.5, -10.5, 10.5,
          (18-3x)/2, (42-6x)/7
)}}}


y = {{{(18-3x)/2}}} is red line;  y = {{{(42-6x)/7}}} is the green line.

  </TD>
  </TR>
</TABLE><pre>The set  {x>0 , y>0} is the first quadrant.

{3x + 2y > 18}    is the domain above the red line.

{6x + 7y < 42}    is the domain below the green line.

So, the intersection is this obtuse tiangle in the first quadrant adjacent to the x-axis.

I do not see much sense in the question of the problem.

You can estimate the range of this linear function z = 3x + 3y by evaluating its values in the vertices of the triangle.
(Then is it typical problem of the linear programming).

May be other tutors have some ideas?
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