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A company that manufactures small canoes has a fixed cost of $18,000. It costs $20 to produce each canoe. The selling price is $80 per canoe. (In solving this exercise, let x represent the number of canoes produced and sold.) For this exercise, a. Write the cost function, C. b. Write the revenue function, R. c. Determine the break-even point. Describe what this means.

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sqdancefan
a) Cost is the total of fixed costs and variable (per unit of product) costs. Of course, the per-unit costs are multiplied by the number of units to determine their total amount.
  C(x) = 18,000 +20x

b) Revenue comes from selling the product. It is the sale price of each product multiplied by the number of products sold.
  R(x) = 80x

c) The break-even point is that point where revenue and cost are equal. That is, revenue from product sales just covers all the costs of producing that product.
  R(x) = C(x)
  80x = 18,000 +20x
  60x = 18000
  x = 18000/60 = 300
The company will break even when it produces and sells 300 canoes.

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