Question 745742
A similar problem was posted a few days ago as problem number 743379.

{{{x}}}= number of tables made per day
{{{y}}}= number of chairs made per day
Two obvious constraints are
{{{x>=0}}} and {{{y>=0}}}
The amount of sawing to be done per day would be
{{{3x+2y<=12}}}.
The amount of assembling work to be done per day would be
{{{x+2y<=8}}}.
The inequalities above graph as a region of the x-y plane representing all the possible combinations of numbers of tables and chairs that they can make daily.
{{{drawing(300,300,-1,9,-1,9,
grid(0),
blue(line(0,6,4,0)),green(line(0,4,8,0)),
locate(4,0.5,C),locate(0.1,0.5,O),locate(-0.5,4.2,A),
locate(2,3.5,B),locate(0.1,6.5,D),locate(8,0.5,E)
)}}} The feasibility region is the quadrilateral OABC, bounded by the lines 
{{{x=0}}} (the y-axis)
{{{y=0}}} (the x-axis)
{{{3x+2y=12}}} (the blue line) and
{{{x+2y=8}}} (the green line).
To plot the blue and green line, I just found the x- and y-intercepts for each one.
For {{{3x+2y=12}}}:
when {{{x=0}}}, {{{3*0+2y=12}}} --> {{{2y=12}}} --> {{{y=12/2}}} --> {{{y=6}}} gives us point D(0,6).
When {{{y=0}}}, {{{3x+2*0=12}}} --> {{{3x=12}}} --> {{{x=12/3}}} --> {{{x=4}}} gives us point C(4,0)
For {{{x+2y=8}}}:
when {{{x=0}}}, {{{0+2y=8}}} --> {{{2y=8}}} --> {{{y=8/2}}} --> {{{y=4}}} gives us point A(0,4).
When {{{y=0}}}, {{{x+2*0=8}}} --> {{{x=8}}} gives us point E(8,0).
The intersection of the 2 lines is the point that satisfies {{{3x+2y=12}}} and
{{{x+2y=8}}}. It is the solution to
{{{system(3x+2y=12,x+2y=8)}}} --> {{{2x=12-8}}} --> {{{2x=4}}} --> {{{x=2}}} and
with {{{system(x=2,x+2y=8)}}} --> {{{2+2y=8}}} --> {{{2y=8-2}}} --> {{{2y=6}}} --> {{{y=3}}}.
That intersection is the point C(2,3).