What is the optimal price and quantity for the monopolist

Question

Let inverse demand be given by P = a - bQ. Let the monopolists total costs be C(Q) = F + cQ.

1. What is the optimal price and quantity for the monopolist?
2. Illustrate this using an appropriate diagram. On the same diagram, also show the marginal revenue curve.
3. What is the elasticity of demand at the point at which the monopolist produces? Can this elasticity take a value between 0 and -1? Justify your answer.
4. What is the dead weight loss (DWL) resulting from this market outcome?
5. Indicate this DWL on an appropriate diagram
6. At what fixed cost would the firm choose to close down?