One very important question facing hospitals is this: How big must a hospital be (in terms of patient-days of care) to minimize the cost per patient-day? According to one well-known study, the total cost (in dollars) of operating a hospital (of a particular type) can be approximated by:
C = 4,700,000 + 0.00013X2
where X is the number of patient- days.
a. Derive a formula for the relationship between cost per patient- day and the number of patient-days.
b. On the basis of the results of this study, how big must a hospital be (in terms of patient-days) to minimize the cost per patient-day?
c. Show that your result minimizes, rather than maximizes, the cost per patient- day.