please help How do you construct a pay of table??????
. Dr. Mike Adams, a local brain surgeon, believes there is a lot of money to be made
renting apartments to students here in Alamosa. He is considering constructing one, two,
or possibly three apartment complexes, each of which contains 40 apartments. Dr.
Adams isn't sure how many to build -that depends on student enrollment. After
checking with the college, Dr. Adams obtained the following projected enrollments:
1500 if there is a decline in the economy; 2250 if there is no change in the economy; and
3000 if the economy increases. About 1/25 of enrolled students will rent from him,
estimates Dr. Adams. This equates to 60 renters if 1500 are enrolled; 90 renters if 2250
are enrolled; and 120 renters if 3000 are enrolled.
The wise and highly respected Dr. Weston was asked to estimate how likely each event
was (i.e. decline, no change, or increase in economy). According to Dr. Weston, a
decline in the economy has a 10% likelihood; no change has a 20% likelihood; and an
increase in the economy has a 70% probability.
Each complex will cost $100,000 per year to build and maintain, or $2,500 per apartment
per year, whether rented or not. He will charge $250 per month rent for all apartments,
which amounts to $3,000 per year per apartment. Thus his profit is $500 per year for
each apartment rented. (Note that he will lose $2500 a year on those he did not rentl)
To construct a pay-off table, you need to analyze the different possible outcomes and their corresponding pay-offs. In this scenario, Dr. Adams is considering building one, two, or three apartment complexes, each with 40 apartments, depending on student enrollment.
To construct the pay-off table, follow these steps:
1. List the possible events: In this case, the events are a decline in the economy, no change in the economy, and an increase in the economy.
2. Determine the probability of each event: Dr. Weston has estimated the probabilities for the events - a 10% likelihood of a decline, 20% likelihood of no change, and 70% probability of an increase in the economy.
3. Calculate the number of renters for each event: Dr. Adams estimates that about 1/25 of enrolled students will rent from him. Using the projected enrollments provided (1500, 2250, 3000), you can calculate the number of renters for each event.
- For a decline in the economy (1500 students), the number of renters would be 1500 / 25 = 60.
- For no change in the economy (2250 students), the number of renters would be 2250 / 25 = 90.
- For an increase in the economy (3000 students), the number of renters would be 3000 / 25 = 120.
4. Calculate the profit for each event: The profit per apartment rented is $500 per year, and the cost per apartment (whether rented or not) is $2,500 per year. Calculate the profit for each event by multiplying the number of renters by the profit per apartment.
- For a decline in the economy, the profit would be 60 renters * $500 profit per apartment = $30,000.
- For no change in the economy, the profit would be 90 renters * $500 profit per apartment = $45,000.
- For an increase in the economy, the profit would be 120 renters * $500 profit per apartment = $60,000.
5. Calculate the total profit for each number of complexes: Since Dr. Adams is considering building one, two, or three complexes, calculate the total profit by multiplying the profit for each event by the number of complexes.
6. Construct the pay-off table: Create a table with rows representing the number of complexes and columns representing the events. Fill in the table with the calculated profits for each situation.
Here's an example of what the pay-off table might look like:
| Number of Complexes | Decline in Economy | No Change in Economy | Increase in Economy |
|---------------------|-------------------|---------------------|---------------------|
| 1 | $30,000 | $45,000 | $60,000 |
| 2 | $60,000 | $90,000 | $120,000 |
| 3 | $90,000 | $135,000 | $180,000 |
Analyzing this pay-off table will help Dr. Adams determine the most profitable decision based on the likelihood of each event and the number of complexes built.