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A company markets exercise DVDs that sell for $19.95, including shipping and handling. The monthly fixed...

A company markets exercise DVDs that sell for $19.95, including shipping and handling. The monthly fixed costs (advertising, rent, etc.) are $19,170 and the variable costs (materials, shipping, etc.) are $6.45 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.
(B) How many DVDs must be sold each month for the company to break even?
1,500 DVDs
(C) Choose the correct graph below:
A. [Graph Image]
B. [Graph Image]
C. [Graph Image]
D. [Graph Image]
What does the region between the lines to the left of the break-even point represent?

Answer

(A) The cost equation is given by: C(x) = 19,170 + 6.45x. The revenue equation is given by: R(x) = 19.95x.

(B) To find the break-even point, set the cost equation equal to the revenue equation: 19,170 + 6.45x = 19.95x. Solving for x gives x = 1,500 DVDs.

(C) The correct graph is not visible, but the break-even point is at 1,500 DVDs. The region to the left of the break-even point represents a loss, as costs exceed revenue. The region to the right represents a profit, as revenue exceeds costs.

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