Question 1101993
create a list as shown below:


<pre>
                           buffet        chair        table        total


cutting                     15            5             10          4900                              
assembly                    20            8              6          6600
finishing                   5             5              6          3900


</pre>


if you let:


x = number of buffets
y = number of chairs
z = number of tables


then your 3 equations that need to be solved simultaneously are:


15x + 5y + 10z = 4900 (equation 1)
20x + 8y + 6z = 6600 (equation 2)
5x + 5y + 6z = 3900 (equation 3)


multiply equation 1 by 3 and equation 2 by 5 to get:


45x + 15y + 30z = 14700 (equation 4)
100x + 40y + 30z = 33000 (equation 5)


subtract equation 4 from equation 5 to get:


55x + 25y = 18300 (equation 6)


leave equation 2 equation 3 as is to get:


20x + 8y + 6z = 6600 (equation 2)
5x + 5y + 6z = 3900 (equation 3)


subtract equation 3 from equation 2 to get:


15x + 3y = 2700 (equation 7)


bring down equation 6 and equation 7.


55x + 25y = 18300 (equation 6)
15x + 3y = 2700 (equation 7)


multiply equation 6 by 3 and 7 by 25 to get:


165x + 75y = 54900 (equation 8)
375x + 75y = 67500 (equation 9)


subtract equation 8 from equation 9 to get:


210x = 12600


solve for x to get x = 12600 / 210 = 60


go back to either equation 6 or equation 7 and solve for y when x  60 to get:


y = 600.


go back to either equation 1 or 2 or 3 and solve for z when x = 60 and y = 600 to get:


z = 100


your solution to all 3 original equations should be:


x = 60
y = 600
z = 100


when x = 60 and y = 600 and z = 100:


15x + 5y + 10z = 4900 (equation 1) becomes 4900 = 4900 which is true.
20x + 8y + 6z = 6600 (equation 2) becomes 6600 = 6600 which is true.
5x + 5y + 6z = 3900 (equation 3) becomes 3900 = 3900 which is true.


the solution is confirmed to be good.


the solution is:


full utilization of resources is satisfied when 60 buffets and 600 chairs and 100 tables are built.