Question 1200628: A factory makes use of two basic machines, A and B, which turn out two different products, yarn and thread. Each unit of yarn requires 1 hour on machine A and 2 hours on machine B, while each unit of thread requires 1 hour on A and 1 hour on B. Machine A runs 8 hours per day, while machine B runs 14 hours per day. How many units each of yarn and thread should the factory make to keep its machines running at capacity?
Answer by ikleyn(52903)   (Show Source):
You can put this solution on YOUR website! .
A factory makes use of two basic machines, A and B,
which turn out two different products, yarn and thread.
Each unit of yarn requires 1 hour on machine A and 2 hours on machine B,
while each unit of thread requires 1 hour on A and 1 hour on B.
Machine A runs 8 hours per day, while machine B runs 14 hours per day.
How many units each of yarn and thread should the factory make
to keep its machines running at capacity?
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Let Y be the number of units of yarn, and
let T be the number of units of thread.
Write equations as you read the problem
1*Y + 1*T = 8 hours (machine A) (1)
2*Y + 1*T = 14 hours (machine B) (2)
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| Thus the setup is complete. |
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To find Y, subtract eq(1) from eq(2). You will get
2Y - Y = 14 - 8 = 6, Y = 6.
Now find T from equation (1)
T = 8 - Y = 8 = 6 = 2.
ANSWER. 6 units of yarn and 2 units of thread.
Solved.
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