Suppose an​ ocean-front hotel rents rooms. In the​ winter, demand​ is:   P1=50−1Q1   with marginal revenue​ of: MR1=50−2Q1.   ​However, in the​ summer, demand​ is: P2=140−1Q2 with marginal revenue​ of:: MR2=140−2Q2.   ​Furthermore, suppose the​ hotel's marginal cost of providing rooms is MC=5+1​Q, which is increasing in Q due to capacity constraints. Suppose the hotel engages in​ peak-load pricing. During the​ winter, the​ profit-maximizing price is  ​$______and the​ profit-maxizing quantity is______rooms.  ​(Enter numeric responses rounded to two decimal​ places.)

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