Question 856006
{{{drawing(300,300,-2,10,-4,8,grid(1),
circle(8,0,0.25),
circle(8,1,0.25),
circle(0,3,0.25),
circle(0,2,0.25),
circle(2,0,0.25),
red(line(8,0,8,10)),graph(300,300,-2,10,-4,8,(12-x)/4,2-x))}}}
Find the points of intersection that bound the region.
(8,0)
(8,1)
(0,3)
(0,2)
(2,0)
The solutions occur at one of these points.
{{{z=x+5y=8+5(0)=8}}}
{{{z=8+5(1)=13}}}
{{{z=0+5(3)=15}}}
{{{z=0+5(2)=10}}}
{{{z=2+5(0)=2}}}
.
.
.

Maximum occurs at (0,3) and equals 15.
Minimum occurs at (2,0) and equals 2.