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.

 

The Trumbull Company has developed a new product. Trumbull’s chairperson

estimates that the new product will increase the firm’s revenues by $5 million

per year, and that it will result in extra out- of- pocket costs of $4 million per

year, the fully allocated costs (including a percentage of overhead, depreciation,

and insurance) being $5.5 million.

a. Trumbull’s chairperson feels that it would not be profitable to introduce

this new product. Is the chairperson right? Why or why not?

b. Trumbull’s vice president for research argues that since the development

of this product has already cost about $10 million, the firm has little

choice but to introduce it. Is the vice president right? Why or why not?