In a physical therapy office, 25 minutes are allowed for regular therapy and 45 minutes are allowed for a in-depth therapy session. A therapist has 7.5 hours (450 minutes) each day for appointments and is only allowed to do 10 in-depth sessions per day. 25 minute sessions cost $80 each and 45 minute sessions cost $120 each. Let x represent the number of 25 minute sessions and y represent the number of 45 minute sessions. Write equations of the constraints and an objective function to model this situation.

Question

In a physical therapy office,  25 minutes are allowed for regular therapy and 45 minutes are allowed for a in-depth therapy session.  A therapist has 7.5 hours (450 minutes) each day for appointments and is only allowed to do 10  in-depth sessions per day.  25 minute sessions cost $80 each and 45 minute sessions cost $120 each.   Let x represent the number of 25 minute sessions and y represent the number of 45 minute sessions.  Write equations of the constraints and an objective function to model this situation.