Real-Life Math
The shareholders on the hospital board are looking for profit. This month, they are counting on you.
You are a hospital administrator for a 150-bed hospital in Chicago. Your job may depend on finding innovative ways to make limited funding go further.
You are funded by a health maintenance organization (HMO) representing 2,000 members. The HMO pays you a fixed amount each month based on how many of its members it predicts you will have to provide care for. You are paid whether they use the service or not.
If you can provide service for one month for less than the amount budgeted by the HMO, your hospital can keep the difference and the hospital board will be happy.
The HMO bases its payment to you on these formulas:
- For each 1,000 clients, 70 will visit your facility for in-patient surgery over the next month. The average cost to treat those patients as calculated by the HMO is $746.
- For every 1,000 clients, 100 will come to your facility for outpatient surgery. The average cost of treating these patients is $459.
How much is the HMO sending in for each member per month? How much is that in total?
You approach your team of surgeons and suggest they do as many surgeries as possible on an outpatient basis without compromising patient care. At the end of the month, you have actually performed 100 surgeries on an in-patient basis and 240 on an outpatient basis. Did you make money? Is your job safe?
Hint:
You've worked some magic and you know that, based on 2,000 clients, the HMO is paying you $104,440 a month for in-patients and $91,800 for outpatients.
0.070 x $746 = $52.22 x 2,000 = $104,440
0.100 x $476 = $45.90 x 2,000 = $91,800
$104,440 + $91,800 = $192,240
Assuming the HMO's cost of delivering the service is correct, you can adjust the formula to determine what you actually spent this month and if there's any profit left over.