Suppose there is a monopolist that produces a homogeneous product and faces the following demand curve: Q = 100 - P. The monopolist's cost function is given by C(Q) = Q^2.

1. What is the monopolist's profit-maximizing output level and price?
2. What is the monopolist's profit at the profit-maximizing output level?
3. Suppose the government imposes a per-unit tax of t dollars on the monopolist's product. What is the new profit-maximizing output level and price?
4. How does the imposition of the tax affect the monopolist's profit?

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