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Question 288487: Regrind, Inc. regrinds used typewriter platens. The variable cost per platen is $1.80. The total cost to regrind 80 platens is $500. Find the linear cost function to regrind platens. If reground platens sell for $10.60 each, how many must be reground and sold to break even?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Regrind, Inc. regrinds used typewriter platens. The variable cost per platen is $1.80.
The total cost to regrind 80 platens is $500.
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You have a slope = 1.8 and a point (80,500)
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Find the linear cost function to regrind platens.
cost = 1.8x + b
Use the point to solve for "b":
500 = 1.8*80 + b
b = 356
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Equation: cost = 1.8x + 356
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If reground platens sell for $10.60 each, how many must be reground and sold to break even?
Revenue = 10.6x
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Break even means Cost = Revenue:
1.8x + 356 = 10.6x
8.8x = 356
x = 40.45
Round down to 40 (the breakeven number of platens)
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Cheers,
Stan H.
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