A monopolist faces the demand function p 100 - q1 q2 and

Question

A monopolist faces the demand function P = 100 - (q1 + q2) and produces identical outputs from two plants with cost function.

C1 = 2q12 C2 = q22.

1. Write down the optimization problem this monopolist has to solve.
2. Write down the first order condition(s).
3. Find how much the monopolist need to produce in each plant to maximize its output.
4. Write down the second order condition(s) and check if they are satisfied.