JNU SSS 2010 Question 18: Monopoly and price discrimination

A monopolist faces the following demand function $D(P)$ : $D(P) = 10 \text{ for } P \text{ in the interval } [0,\ 10]$ $= 20 - P \text{ for } P \text{ in the interval } (10,\ 20)$ $= 0 \text{ for } P \text{ in the interval } [20,\ \infty)$ Now suppose that the monopolist has zero-variable cost of production. However, if it produces any positive amount, it must incur a fixed cost of Rs 50. What is the optimal monopoly price?