To determine the most efficient size of a hospital, we need to consider the relationship between the number of patients and the average cost of operation.
Let's calculate the total cost of operation for each hospital first:
Hospital A:
Total cost = Number of patients * Average cost per day
Total cost for Hospital A = 500 * $1500 = $750,000
Hospital B:
Total cost for Hospital B = 300 * $600 = $180,000
Hospital C:
Total cost for Hospital C = 100 * $600 = $60,000
Now let's represent the relationship between the number of patients and the total cost for each hospital on a graph:
Cost ($)
$800,000 +-----------------------------------------------------------------------+
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| Hospital A |
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$750,000 +-----------------------------------------------------------------------+
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$600,000 +-----------------------------------------------------------------------+
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| Hospital B |
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$300,000 +-----------------------------------------------------------------------+
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$60,000 +-----------------------------------------------------------------------+
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| Hospital C
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+-----------------------------------------------------------------------+
0 200 400 600
Number of Patients
In this graph, the x-axis represents the number of patients, and the y-axis represents the total cost of operation.
From the graph, we observe that as the number of patients increases, the total cost of operation increases for each hospital. However, Hospital A has a steeper slope compared to the other two hospitals, indicating that a larger increase in the number of patients leads to a relatively larger increase in total cost.
Therefore, we can conclude that the most efficient size of a hospital is closer to Hospital B or C, with 300 or 100 patients per day, respectively. These hospitals have a lower average cost per patient and a lower total cost of operation compared to Hospital A.
It's important to note that the choice of hospital size also depends on other factors such as demand, available resources, and economies of scale. This analysis is based solely on the given average costs and number of patients.