Suppose that a monopolist is producing a product that has a fixed cost of $10,000 and a variable cost of $20 per unit. The market demand for the product is given by the following inverse demand curve:

P = $100 - Q$

where P is the price of the product and Q is the quantity of the product.

The monopolist's objective is to maximize profit.

1. Find the monopolist's profit-maximizing price and quantity.

2. Calculate the monopolist's total profit.

3. Calculate the consumer surplus at the profit-maximizing price and quantity.

4. Calculate the producer surplus at the profit-maximizing price and quantity.

5. Calculate the total surplus (consumer surplus + producer surplus) at the profit-maximizing price and quantity.

6. Suppose that the government implements a price ceiling at the profit-maximizing price. How will this policy affect the monopolist's profit, consumer surplus, and total surplus?