Here’s a particularly useful list of rules for calculating (math) derivatives (taken from the “Optimization” reading assignment):

# Category Archives: Helpful Hints

# Problem Set 1 hint…

Problem Set 1 is due at the beginning of class on Tuesday, January 16. Here is a hint for solving the 4th question on problem set 1.

The objective is to determine how big a hospital must be so that the *cost per patient-day* is minimized. We are not interested in minimizing total cost; if this were the case, there would be no hospital because marginal costs are positive, which implies that total cost is positively related to the number of patient-days.

The cost equation *C* = 4,700,000 + 0.00013*X*^{2} tells you the total cost as a function of the number of patient-days. This is why you are asked in part “a” of the 4th question to derive a formula for the relationship between cost per patient-day and the number of patient days. Once you have that equation, then that is what you minimize, and you’ll be able to answer the question concerning optimal hospital size.