One very important question facing hospital is: How big must a hospital be (in terms of...

Question:

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.

Profit:

Profit is the difference between total revenue and total cost. Total revenue is the revenue which is generated by selling a given quantity of output. Total cost is the cost which is incurred in the process of production.

Answer and Explanation: 1

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a) As we know

{eq}\begin{array}{c} C = 4700000 + 0.00013{X^2}\\ {\rm{Cost per patient }}\\ Y = \frac{C}{X}\\ Y = \frac{{4700000 +...

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Total Cost in Economics: Definition & Formula

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Chapter 3 / Lesson 16
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What is total cost in economics? Learn how to calculate total cost using the total cost formula. See the definitions of total fixed cost and total variable cost.


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