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600​-room hotel can rent every one of its rooms at ​$80 per room. For each​ $1...

600​-room hotel can rent every one of its rooms at ​$80 per room. For each​ $1 increase in​ rent, 6 fewer rooms are rented. Each rented room costs the hotel​ $10 to service per day. How much should the hotel charge for each room to maximize its daily​ profit? What is the maximum daily​ profit?

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