A sanatorium that taking care patients after surgery faces somewhat seasonal demand. As a result, the forecast of patient days of demand is as follows (patient day is one patient staying for one day in the sanatorium):

	Spring	Summer	Fall	Winter
Forecast (Patient day)	90000	70000	85000	60000

The sanatorium uses regular attendants, part-time attendants (when the sanatorium can get them), and contract attendant (who are not employees). Contract attendants work a number of hours which varies depending on their contract established with the sanatorium. Regular attendants are paid a sum of $8,000 per quarter for 60 days of work; part-time attendants are paid $3,500 per quarter for 30 days of work. Contract attendants get an average of $9,000 per quarter for 60 days of work. It costs $1,000 to hire or lay off any of these three types of attendants. Suppose that regular attendants are set at a level of 800 attendants for the year. Each regular attendant works the equivalent of 60 days per quarter. The remainder of the demand is made up by 50 percent part-time and 50 percent contract attendants on a quarter-by-quarter basis. Assume it takes 0.8 attendant day to provide around-the-clock care for each patient day.

(a) What is the cost of this plan starting at the beginning of spring with a level of 800 regular attendants, 200 part-time attendants and 200 contract attendants?

(b) Suppose regular attendants are still set at a level of 800 attendants for the year. What is a better mixed of the part-time and contract attendants on a quarter-by-quarter basis, in terms of percentage that the total cost will be the lowest? What condition(s) should be considered?