Question: Suppose you are a monopolist operating two plants at different locations. Both plants produce the same product; \[{{Q}_{1}}\] is the quantity produced at plant 1, and \[{{Q}_{2}}\] is the quantity produced at plant 2. You face the following inverse demand function: \[P=500-2Q\] , where \[Q={{Q}_{1}}+{{Q}_{2}}\] . The cost functions for the two plants are \[{{C}_{1}}=25+2Q_{1}^{2}\] ; \[{{C}_{1}}=20+Q_{2}^{2}\] .

1. What are your marginal revenue and marginal cost functions?
2. To maximize profits, how much should you produce at plant 1? At plant 2?
3. What is the price that maximizes profits?
4. What are the maximum profits?

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