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A company markets exercise DVDs that sell for $14.95, including shipping and handling. The monthly fixed...

A company markets exercise DVDs that sell for $14.95, including shipping and handling. The monthly fixed costs (advertising, rent, etc.) are $11,440 and the variable costs (materials, shipping, etc.) are $8.45 per DVD.
(A) Find the cost equation and the revenue equation.
(B) How many DVDs must be sold each month for the company to break even?
(C) Graph the cost and revenue equations in the same coordinate system and show the break-even point. Interpret the regions between the lines to the left and to the right of the break-even point.
This number of DVDs that must be manufactured to break even
The profit when x DVDs are manufactured.
The loss when x DVDs are manufactured.
The number of DVDs manufactured.
What does the region between the lines to the right of the break-even point represent?
The loss when x DVDs are manufactured.
The profit when x DVDs are manufactured.
The number of DVDs manufactured.
The number of DVDs that must be manufactured to break even.

Answer

  1. (A) Cost Equation: C(x) = 11440 + 8.45x
    Revenue Equation: R(x) = 14.95x

  2. (B) Break-even Point: Set C(x) = R(x)
    11440 + 8.45x = 14.95x
    11440 = 6.5x
    x = 1760 DVDs

  3. (C) Graph Interpretation: The break-even point is at 1760 DVDs. To the left of this point, the company incurs a loss, and to the right, the company makes a profit.

  4. The region between the lines to the right of the break-even point represents the profit when x DVDs are manufactured.

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