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Question 1101993: 7. Irfan Furniture makes dining room furniture. A buffet requires 15 hours for cutting, 20 hours for assembly and 5 hours for finishing. A chair requires 5 hours for cutting, 8 hours for assembly and 5 hours for finishing. A table requires 10 hours for cutting, 6 hours for assembly and 6 hours for finishing. The cutting department has 4900 hours of labor available each week, the assembly department has 6600 hours of labor available, and the finishing department has 3900 hours of labor available. How many pieces of each type of furniture should be produced each week if the factory is to run at full capacity?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! create a list as shown below:
buffet chair table total
cutting 15 5 10 4900
assembly 20 8 6 6600
finishing 5 5 6 3900
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.
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