Answer:
To find out the maximum utilization of days per 1,000 members before the nursing home begins to lose money, we need to compare the revenue from the HMO contract to the expected costs.
Given:
- Revenue per member per month (PMPM) = $2.00
- Average cost per day = $120
First, let's convert the revenue to a daily rate:
Revenue per day per member = Revenue PMPM / 30 days
\(= \frac{2}{30} = \frac{1}{15} \) dollars
Next, we need to find out how many days a member can stay before the nursing home begins to lose money:
\( \text{Max days} = \frac{\text{Total Revenue}}{\text{Average Cost per Day}} \)
\( \text{Max days} = \frac{\frac{1}{15} \text{ dollars}}{120 \text{ dollars}} \)
\( \text{Max days} \approx 0.111 \)
To convert this to days per 1,000 members, we multiply by 1,000:
\( \text{Max days per 1,000 members} = 0.111 \times 1000 \approx 111 \)
So, the nursing home can experience a maximum utilization of 111 days per 1,000 members before it begins to lose money.
Explanation: