Question 205208
A furniture maker has a shop that can employ 12 workers for 40 hour per week at
 its maximum capacity. The shop makes tables and chairs. 
It takes 16 hours of labor to make a table and 8 hours of labor to make a chair. 
Graph the region that shows the possibilities for the number of tables and
 chairs that could be made in one week.
:
Total man-hours per week: 12*40 = 480 hrs
:
x = no. of tables, y = no. of chairs
:
16x + 8y =< 480
Put in equation into the slope intercept form for graphing
8y =< -16x + 480
y =< -(16/8)x + (480/8)
y =< -2x + 60
:
Graph it from x = 0 to x = 30 
:
 x | y 
-------
 0 | 60; all chairs
10 | 40
20 | 20
30 |  0; all tables 
:
Your graph should look this:
{{{ graph( 300, 200, -6, 36, -6, 66, -2x+60 ) }}}
:
The area of feasibility would be the positive region at or below the line
: