SOLUTION: 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,

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(52792) (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?
~~~~~~~~~~~~~~~~~~

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)


     +--------------------------------+
     |   Thus the setup is complete.  |
     +--------------------------------+


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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