Problem Set 1 Helpful Hints | Business Risk Management

Here are some homework hints for problem set 1. The first two problems involve straightforward applications of the ?Calculating Derivatives? rules listed on page 22 of the Mathematics Tutorial.? In the third problem, you need to compute partial derivatives.? The logic for partial derivatives is laid out on page 25 of the Mathematics Tutorial.? Basically, when you partially differentiate a function, you are studying how the function changes when one variable changes, holding everything else constant.? Finally, in the?fourth problem, 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 + 0.00013X^2 tells you the total cost as a function of the number of patient-days. This is why you are asked in part ?a? 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.

Source: http://risk.garven.com/2012/08/23/problem-set-1-helpful-hints/

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