Textbook Problem

The cost per day of running a hospital is 300,000 + 0.75x² dollars, where x is the number of patients served per day. What number of patients served per day minimizes the cost per patient per day of running the hospital if the hospital’s daily capacity is 200 patients? How does the solution change as the hospital’s capacity increases? Let capacity increase from 200 to 500 in increments of 25.