# profit maximization

You have an: Los Angeles and Brooklyn. You produce all the jerseys in a single factory located in Seattle. Your total cost function associated with producing the baseball jerseys is c(Q)=Q2+400 where q is the total amount of jerseys you produce. The inverse demand function for your jerseys in Los Angeles is PLA(QLA)=60-QLA where qLA is the quantity of jerseys sold in Los Angeles. The inverse demand function in Brooklyn is PB(QB)=40-2QB. Assume there is no transportation costs.

How many baseball jerseys will you sell in Los Angeles and how many in Brooklyn? What will be the price of your jersey in Los Angeles and what will be the price in Brooklyn? What will be your total profits?

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#### Solution Preview

we use the rule MR = MC

MC is easy to calculate, it is simply the derivative of the cost function, which is 2Q.

MR is different in both places, we calculate them separately. I use QL and QB to differentiate LA and ...