First degree price discrimination question

1, (1DPD) A monopolist faces the inverse market demand curve P = 6 - Q, and the total cost function C = 2Q. The firm's marginal cost is therefore MC = 2. Assume the demand curve is made up of many consumers each with unit demand for this good (i.e. each consumer will either buy one or nothing and the market demand curve is the aggregation of all these unit-demand consumers.)

• a, If the monopolist cannot price discriminate, find the monopolist's price, quantity, profit, and consumer surplus.
• b, What assumptions are necessary for the monopoly to be able to perfectly price discriminate (1DPD)?
• c, If the monopolist can perfectly price discriminate, solve for its profits, and total consumer surplus. (Hint: since consumers have unit demand, all three methods - separate prices per unit, package prices, or a two-part tariff are trivially the same. For example, the "package" contains exactly one good, and every consumer receives a price equal to her valuation.)

Please answer the questions with all the steps and calculations