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here is the problem.
In planning for a new item, a manufacturer assumes that
the number of items produced x and the cost in dollars C of producing these items
are related by a linear equation. Projections are that 100 items will cost $10,000 to
produce and that 300 items will cost $22,000 to produce. Find the equation that
relates C and x.
As the equation is linear, your answer is going to be of the form C = ax + b, and you need to find out what those constants are.
The given information can help you to find these.
100a+b = 10000
300a+b = 22000
Taking the first equation away from the second gives 200a = 12000.
From this we can deduce that a = 60.
Now we know a, we can easily substitute that into one of the original equations to find b.
100*60 + b = 10000
b = 4000.
Therefore, your equation is C = 60a+4000.
Or C = 20(3a+200) if you want to make it a bit neater, but that bit's not necessary.
Why did the vector cross the road?
It wanted to be normal.
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