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A company that manufactures small canoes has a fixed cost of 18,000. It costs 100 to produce each canoe. The selling price is $400 per canoe. (In solving this exercise, let x represent the number of canoes produced and sold.) C(x)=18,000+100x R(x)=400x What is the breakeven point?

Mathematics

ScanSolve AI Answer

Answer

60 canoes60 \text{ canoes}

Graph of R(x) = 400x

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Key points of R(x) = 400x
Pointxy
x-intercept00

Step-by-step solution

4 steps
  1. Understand the breakeven point.

    The breakeven point is when the total cost equals the total revenue. This means C(x)=R(x)C(x) = R(x).

  2. Set the given cost and revenue functions equal to each other.

    The cost function is C(x)=18000+100xC(x) = 18000 + 100x.
    The revenue function is R(x)=400xR(x) = 400x.

    18000+100x=400x18000 + 100x = 400x
  3. Solve the equation for xx.

    Subtract 100x100x from both sides of the equation:

    18000=400x−100x18000 = 400x - 100x 18000=300x18000 = 300x
  4. Isolate xx by dividing both sides by 300.

    x=18000300x = \frac{18000}{300} x=60x = 60

    The breakeven point is when 60 canoes are produced and sold.

    60 canoes60 \text{ canoes}
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