Question 704294
{{{x+2y>=14}}}
{{{2x+y>=16}}}
{{{x>=0}}}
{{{y>=0}}}
The boundary lines are the x- and y-axes ({{{y=0}}} and ({{{x=0}}} respectively)
and the lines {{{x+2y=14}}} and {{{2x+y=16}}}
Those lines intersect at
{{{system(x+2y=14,2x+y=16)}}} --> {{{x=6}}} and {{{y=4}}} for point (6,4)
The axes intersect at the origin, of course.
The lines intersect the axes at points with x=0 and y=o, and we can find the other coordinate by substituting those zeros.
For {{{x+2y=14}}} we find the intercepts as (0,7) and (14,0)
{{{x=0}}} --> {{{2y=14}}} --> {{{y=7)))
{{{y=0}}} --> {{{x=14}}}
For {{{2x+y=16}}} we find the intercepts as
{{{x=0}}}--> {{{y=16)))
{{{y=0}}} --> {{{2x=16}}} --> {{{x=8}}}
 
GRAPHING:
{{{drawing(300,300,-2,18,-2,18,
grid(0),
line(0,7,14,0),line(0,16,8,0),
locate(0.2,1.1,O),locate(0.1,8,B(0,7)),locate(6.1,5,C(6,4)),locate(8.2,1.1,D)
)}}} The feasible set is the quadrilateral OBCD.