solution

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.