Chapter 18 Exercises
Solution to Textbook Exercise 18-1.
1. The first task in solving this problem is to organize the data. Below are the facts and constraints relevant to solving this exercise.
Facts and Constraints
| Item # | Data |
| 1. | 10 to 20 teams |
| 2. | double round-robin league |
| 3. | 5 lighted diamonds |
| 4. | 2 games per diamond per evening |
| 5. | play 3 evenings per week |
| 6. | 1/2 of games under lights |
2. The next task is to classify costs as fixed, changing fixed, or variable.
Fixed Costs: Fixed costs are classified as either indirect or direct costs.
| Item # | Cost Data | Amount |
| P.S. | Indirect agency: $80,000/5 = 16,000/20 = | $ 800 |
| P.S. | Indirect unit: $26,000/20 = | 1300 |
| 10 | Direct: catcher's equipment: 180 x 5 = | 900 |
| 13 | Direct: trophies: | 100 |
| Total Fixed Costs (10 through 20 teams) | $3,100 |
Changing Fixed Costs: In this problem, it is most convenient to handle the following costs as changing fixed costs. Because of the nature of a round-robin tournament, the number of games to be played is not solely a function of adding another team (which would make it a variable cost). The number of games to be played is also dependent on the number of teams already included. The formula for calculating the number of games to be played in a double round-robin tournament is: (n) x (n-1) with n = the number of teams to play in the tournament.
| Item # | Cost Data | Amount |
| 6 | Umpires: 12 x 2 = | $ 24 |
| 8 | Balls: 3 x1 = | 3 |
| 11 | Lights: 10 x 2 = 20/2 = | 10 |
| 12 | Diamond maintenance: 20/2 = | 10 |
| ___________ | ||
| $47/game |
Variable Costs: Variable costs in this problem are costs that are the same for each team added to the league. Bats and score books are the only true variable costs.
| Item # | Cost Data | Amount |
| 7 | Bats: 8 x 4 = | $ 32 |
| 9 | Score books: 1.50 x 2 = | 3 |
| ___________ | ||
| $35/team |
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Cost-Volume-Profit Table for
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»Number of games required to complete the tournament:
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10 = (10) (10-1) = (10) (9) = 90
15 = (15) (15-1) = (15) (14) = 210
20 = (20) (20-1) = (20) (19) = 380
Answers to questions:
1. Total Costs for 20 teams are $21,660. (See column 3 in Table for details).
2. Difference in Costs between 20 and 10 teams is: $21,660 - $7,680 = $ 13,980. (This difference is made up of the increasing number of games that must be played with the addition of each new team to a round-robin league).
3. Overhead costs for the league include $800 in center administrative overhead plus $1,300 in unit overhead costs = $2,100.
4. Variable costs of the program include the costs incurred by team: that is, $32/team for bats plus $3/team for score books = $35/team.
5. Break-even table for a 20-team single round robin tournament. Formula for calculating the number of games needed for a 20-team single round robin is (n) (n-1) / 2. Therefore (20) (20-1) / 2 = (20) (19) / 2 = 380/2 = 190 games.
| Fixed costs for 20 teams | |
| Center | $ 800 |
| Division | 1,300 |
| Trophies | 100 |
| Catchers equipment | 900 |
| Changing Fixed Costs | |
| $47/game x 190 games | 8,930 |
| Variable costs | |
| $35/team x 20 teams | 700 |
| Total Costs | $12,730 |
| $12,730/20 teams = $636.50/team | |
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6. $1,083.00/team Double round-robin - 636.50/team Single round-robin $- 446.50/team Difference |
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Note: The difference in cost between the 20-team double round-robin league versus the 20-team single round-robin is $466.50 per team or $8,930 [20 x $466.50 = $8,930]. This is exactly the cost of playing 190 games [$47/game in changing fixed costs x 190 games = $8,930]. The point here is that a round-robin programming format adds costs very rapidly because of each team needing to play every other team in each round. In fact it would be much cheaper to play two 10-team double round-robin leagues than it is to play one 20-team double round-robin league. If you want to impress your instructor, calculate these costs and demonstrate why this is so!
Source: Dr. Jerry Burnam, College of Applied Life Studies, University of Illinois, Urbana-Champaign
Copyright © 2003 J.R. Rossman (jrrossm@ilstu.edu)& B.E. Schlatter (beschla@ilstu.edu)