1. The publisher of an medical newsletter estimates that with x thousand subscribers its monthly revenue and cost (in thousands of dollars) are given by the following:

R(X)
= 32x - .21x^{2}

C(x) = 195 + 12x

Determine the number of subscribers needed for the publisher to break-even.

Solution:

Profit equals revenue less cost. The breakeven point occurs where profit is zero or when revenue equals cost.

Profit = R(x) - C(x)

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set profit = 0

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Solve using the quadratic formula where a = 195, b = 20, and c = .21.

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Breakeven points occur where the publisher has either 12,000 or 84,000 subscribers. Between these two points the publisher will be profitable.

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