Regrind, Inc. regrinds used typewriter platens. The cost per platen is $1.30. Th

Question

Regrind, Inc. regrinds used typewriter platens. The cost per platen is $1.30. The cost to regrind 110 platens is $500. Find the linear cost function to regrind platens. If reground platens sell for $10.80 each, how many must be reground and sold to break even? Northwest Molded molds plastic handles which cost $1.00 per handle to mold. The fixed cost to run the molding machine is $3417 per week. If the company sells the handles for $4.00 each, how many handles must be molded weekly to break even?

Explanation / Answer

Regrind, Inc. regrinds used typewriter platens. The variable cost per platen is $1.30.
The total cost to regrind 110 platens is $500.

You have a slope = 1.3 and a point (110,500)

Find the linear cost function to regrind platens.
cost = 1.3x + b
Use the point to solve for "b":
500 = 1.3*110 + b
b = 357
Equation: cost = 1.3x + 357

Here reground platens sold for $10.80 each. Then we have to find reground and sold to break even.
Revenue = 10.8x

Break even means Cost = Revenue:

1.3x + 357 = 10.8x
8.5x = 357
x = 42

42 must be reground and sold to break even.

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