Suppose hospital (A) has 500 patients/day and average cost of operation is $1500/day. Hospital (B) has 300 patients/day and average cost of $600/day. Hospital (C) has 100 patients/day and average cost of $600/day. What can you say about the most efficient size of hospital? Explain the reasons for this choice of hospital size. Illustrate your answer with a graph.
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.
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. In this case, we have three hospitals: A, B, and C, with different numbers of patients and average costs per day. Let's analyze each hospital's efficiency based on their costs and patient volumes.
First, let's calculate the total cost for each hospital per day:
Total cost for Hospital A = 500 patients/day * $1500/day = $750,000/day
Total cost for Hospital B = 300 patients/day * $600/day = $180,000/day
Total cost for Hospital C = 100 patients/day * $600/day = $60,000/day
From the information given, we can see that Hospital A incurs the highest total cost per day, followed by Hospital B and then Hospital C.
To illustrate this, we can create a graph with the number of patients on the x-axis and the total cost on the y-axis.
Let's plot the three hospitals on the graph:
- Hospital A: 500 patients/day, $750,000/day
- Hospital B: 300 patients/day, $180,000/day
- Hospital C: 100 patients/day, $60,000/day
The graph will show a positive linear relationship where the number of patients increases as we move along the x-axis, and the total cost increases as we move along the y-axis.
The graph will display a line with a positive slope, indicating that as the number of patients increases, the total cost also increases. We can observe that Hospital A has the steepest slope, followed by Hospital B, and Hospital C has the shallowest slope.
Based on the information and the graph, we can conclude that having a smaller number of patients leads to lower total costs. Therefore, Hospital C with 100 patients/day is the most efficient in terms of cost as it has the lowest total cost among the three hospitals.
It is important to note that this analysis is solely based on the given information and the relationship between patient volume and cost. Other factors, such as quality of care, specialization, and revenue generation, should also be considered when determining the efficiency of a hospital.