Question 251014
Graph the constraints to find the feasible region.

{{{x>=2}}}
{{{y>=0}}}
{{{x+y<=6}}}
{{{y<=6-x}}}
{{{drawing( 300, 300, -2, 8, -2, 8,grid( 1 ),circle( 2, 0, .2 ),
circle(6,0,0.2),
green(line(6,0.1,2,0.1)),
green(line(2,0,2,4)),
green(line(2.05,4.05,6.05,0.05)),
circle(2,4,0.2),graph( 300, 300, -2, 8, -2,8, 6-x)) }}} 
As we see the feasible region is a triangle with vertices at (2,0),(2,4),and (0,6).
The max and min of the objective function occurs at one of these vertices.
(2,0): {{{ z=3x+5y=3(2)+5(0)=6}}}
(2,4): {{{ z=3x+5y=3(2)+5(4)=26}}}
(6,0): {{{ z=3x+5y=3(6)+5(0)=18}}}
The max value of 26 occurs at (2,4).