Question 565054: Acme parts can produce padiator seal kit for $7.50 with fixed set-up costs of $395. They plan to market the radiator seal kits for $22.95. Find the linear cost function
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! It costs $395 to get the tools/equipment you need just to start, before you manufacture anything.
After that, it costs $7.50 to make each kit, so making x kits costs $7.5 times x, on top of your original $395 investment.
The cost to produce  seal kits (in $) is
 , and that's your answer.
Going a little further:
It will take making and selling a few kits to break even. If you sell x of them at $22.95 each, you would get $22.95 times x in sales. In $, that is  .
To break even, that should equal the cost of making x kits, so
Solving that equation
-->  -->  -->  -->  --> x=about 25.6
If you make and sell 25 kits you will have a tiny loss.
If you make and sell 26 kits you will have a tiny profit.
Looking at it graphically, your cost and sales as a function of number of kits produced and sold can be plotted like this
 C(x) in red, S(x) in green
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