Suppose a monopoly at a price. For political reasons, the company produces in three different sites (factories). The cost structure of installations 1, 2 and 3 is as follows.

C₁(Q₁) = 15Q₁²-Q₁ C₂(Q₁, Q₂) = 10Q₂²-Q₁Q₂ C₃(Q₃) = 5Q₃2 respectively. Q₁ is the production produced at installation 1, Q₂ is the production produced at installation 2 and Q₃ is the production produced at installation 3. The company faces the following demand: P=10,000-5Q

Where Q is the total output produced by the firm

Set up the profit maximization problem(s)?