Question 1067023: A furniture company makes large and small chairs. A small chair takes 30 minutes of machine time and 60 minutes of labor to build. A large chair takes 45 minutes of machine time and 80 minutes of labor to build. The company has 64 hours of labor time and 34 hours of machine time available each day. How Many of each type of chair is built in a day?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! it looks like you want a solution that uses exactly the number of hours of machine time and labor time available.
a small chair takes 30 minutes of machine time and 60 minutes of labor.
a large chair takes 45 minutes of machine time and 80 minutes of labor.
you have a total of 34 hours of machine time available.
you have a total of 64 hours of labor time available.
let x = number of small chairs.
let y = number of large chairs.
your constraint equations are:
machine time:
30x + 45y = 34*60
labor time:
60x + 80y = 64*60
the total machine time and labor time are converted to minutes by multiplying them by 60.
the equations become:
30x + 45y = 2040
60x + 80y = 3840
solve these 2 equations simultaneously and you'll get the number of small and large chairs that can be built with those available hours.
multiply the first equation by 2 and leave the second equation as is to get:
60x + 90y = 4080
60x + 80y = 3840
subtract the second equation from the first to get:
10y = 240
solve for y to get y = 24
since 30x + 45y = 2040, and since y = 24, then replace y with 24 and you get:
30x + 45*24 = 2040
simplify to get 30x + 1080 = 2040
subtract 1080 from both sides of the equation to get:
30x = 960
solve for x to get x = 32
your solution is that x = 32 and y = 24.
that means 32 small chairs and 24 large chairs can be built based on the constraints.
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