Please help me with a specific solution

4) [20 points] A tennis club has two types of customers : \"senior players\" and \"junior players\". The club knows that there is an equal number of senior players and junior players. The club incurs a xed cost per month independent of the time the courts are used (there are no variable costs). Junior players have a monthly demand function q = 40 p and senior players have a demand function q = 10 30/4, where q is the court time (in hours) and p is the court rate (price per hour). (a) Initially the club charges a court rate p to all the players. What court rate maximizes the club's prots? At that price, how many hours does a senior player and a junior player play? (b) The manager of the club decides to change the fees it charges the players. The manager can distinguish senior players from junior players by the information they must provide when they join the club. So the manager sets two different court rates: pa for senior players and p5; for junior players. What prices p3 and 333- maximize the club's prots? -\\ fan I I 'I I 'II . 0.1 . ll .0 n! \\