Consider a monopolist that has a constant marginal cost of $1 per unit. The demand for the product has a choke price of $9. If the price was $4, the quantity demanded would be 5. Suppose that the monopolist wishes to maximize their profit by choosing quantities.

1. Write down the maximization problem of the monopolist, when they choose quantities.

2. What is the quantity produced by the monopolist?

3. What price will the monopolist charge?

4. What is the profit of the monopolist?