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 - .21x2
C(x) = 195 + 12x
Determine the number of subscribers needed for the publisher to break-even.
Profit equals revenue less cost. The breakeven point occurs where profit is zero or when revenue equals cost.
Profit = R(x) - C(x)
set profit = 0
Solve using the quadratic formula where a = 195, b = 20, and c = .21.
Breakeven points occur where the publisher has either 12,000 or 84,000 subscribers. Between these two points the publisher will be profitable.