Playlandat thePNEis an amusement park in Vancouver (https://www.pne.ca/playland/). The guests who are 48'' or taller can go on any ride they want and so they get more value from visiting the park; let us say their individual demand is given byP= 4 - 0.2q_T, wherePis the price per ride ($ per ride) andq_Tis the number of the rides (per day per guest) (the subscriptTstands for "Thrill Seeker Pass;" that's how the park calls its passes for the guests who are 48'' or taller). The guests who are under 48'' are not allowed on certain rides so they get less value from visiting the park; let us say their individual demand is given byP= 3.6 - 0.2q_F, wherePis the price per ride ($ per ride) andq_Fis the number of the rides (per day per guest) (the subscriptFstands for "Fun Pass;" that's how the park calls its passes for the guests under 48''). Assume it costs the park flat 20 per guest to operate a single ride, and it costs the park flat 40 to issue a single ticket to a ride. Assume there are 500 guests 48'' or taller and 500 guests under 48'' on an average day.Playlandis a monopolist amusement park in Vancouver.

1.IfPlaylandemployed a two-part tariff scheme (the park may choose to ticket each ride, or they may choose to let people go on as many rides [at zero price per ride] as they want and only charge the gate fee for the access to the rides),

a.what would be the gate entry fee for guests 48'' or taller ($ per guest) and what would be the gate entry fee for guests under 48'' ($ per guest)?

b.what would be the price per ride ($ per ride)?

c. what isPlayland's profit on an average day ($ per day)? Assume zero fixed cost.