SOLUTION: A furniture company makes large and small chairs. A small chair takes 20 minutes of machine time and 60 minutes of labor to build. A large chair takes 50 minutes of machine time an

Question 1102287: A furniture company makes large and small chairs. A small chair takes 20 minutes of machine time and 60 minutes of labor to build. A large chair takes 50 minutes of machine time and 90 minutes of labor to build. The company has 60 hours of labor time and 26 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!
x = number small chairs.
y = number of large chairs.

60 hours of labor time = 3600 minutes.

26 hours of machine time = 1560 minutes.

you are told that:

a small chair takes 20 minutes and a large chair takes 50 minutes of machine time.

a small chair takes 60 minutes and a large chair takes 90 minutes of labor.

since it appears that you want to make full utilization of the resources available to you, then your equations become:

20x + 50y = 1560
60x + 90y = 3600

the first equation tells you that 20 minutes of machine time * the number of small chairs + 50 minutes of machine time * the number of large chairs needs to be equal to 1560 minutes of machine time available.

the second equaiton tells you that 60 minutes of labor * the number of small chairs + 90 minutes of labor * the number of large chairs needs to be equal to 3600 minutes of machine time available.

you need to solve these two equations simultaneously.
this means the same solution applies to both equations.

multiply both sides of the first equation by 3 and leave the second equation as is to get:

60x + 150y = 4680
60x + 90y = 3600

subtract the second equation from the first to get 60y = 1080

solve for y to get y = 18

use either original equation to solve for x.

you will get x = 33.

check both original equations to see that they are true with these value of x and y.

20x + 50y = 20*33 + 50*18 = 1560 which is true.
60x + 90y = 60*33 + 90*18 = 3600 which is also true.

the solution looks good.

you will maximize your utilization of resources when x = 33 and y = 18.

this means when you build 33 small chairs and 18 large chairs.

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