One very important question facing hospital is: How big must a hospital be ( in terms of patient-days of care) to minimize the cost per patient-day?

1. One very important question facing hospital is: 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.

1. The Miller Company uses skilled and unskilled labor to do a particular construction project. The cost of doing the project depends on the number of hours of skilled labor and the number of hours of unskilled labor that are used, the relationship being:

 C = 4 -3X1 – 4X2 + 2X12 + 3X22+ X1X2, where C is cost (in thousands of dollars) , X1 is the number of hours (in thousands) of skilled labor and X2 is the number of hours (in thousands) of unskilled labor.

a) Find the number of hours of skilled labor and the number of hours of unskilled labor that will minimize the cost of doing the project.

If the Miller Company has to purchase a license costing $2,000 to do this project (and if the cost of this license is not included in C), will this alter the answer to part a? If so, how will the answer change?

b. On the basis of the results of this study, how big must a hospital be (in terms of patient-days) tominimize the cost per patient-day? c) Show that your result minimizes, rather than maximizes,...