SOLUTION: A furniture maker has a shop that can employ 12 workers for 40 hours per week at its maximum capacity. The shop makes tables and chairs. It takes 16 hours of labor to make a table

Question 205208: A furniture maker has a shop that can employ 12 workers for 40 hours 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.
I am completely lost on this problem. Any help provided, is greatly appreciated...Thanks!!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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:

:
The area of feasibility would be the positive region at or below the line
:

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