Problem:
The Tennessee Pterodactyls (I would like a detailed analysis of the problem--broken down to simplistic understanding--and how the solution was derived in similar simple to understand terms.)
The Tennesse Pterodactyls is a new professional basketball franchise in Nashville. The team's general manager, Jerry East, and coach, Phil Riley, are trying to develop a roster of players. They drafted seven players from a pool to which the other teams in the league each contributed two players. However, the general manager and coach perceive these acquisitions to be no more than role players.
They believe that the nucleus of their new team must come from the free agents who are currently available on the market. The team is well under the salary cap, and the owner has made $50 million per year available to them to sign players. The coach and general manager have put together the attached list of free agents, with important statistics for each, including their rumored asking price in terms of annual salary (See attachment)
Jerry and Phil want to sign five free agents. They would like the group they sign to average at least 80 points per game (16 points per player), pull down an average of 40 rebounds per game (8 per player), dish out an average of 25 assists, and have averaged 190 minutes (38 minutes per player) per game in the past. Furthermore, they do not want to sign more than two front court and three back court players. Their immediate objective is to identify the players who as a group would meet their objectives at the minimum cost.
A. Formulate an integer linear programming model to help the general manager and coach determine which players they should sign and solve it by using the computer.
B. Is the money provided by the owner sufficient to sign the group of players identified in (A)? If not, reformulate the model so that the available funds are a constraint and the objective is to maximize the average points of the group.
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Per- Game Averages |
|
Projected
Annual Salary
($1,000,000s) |
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| Player |
Position |
Points |
Rebounds |
Assists |
Minutes |
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| 1. Mack Madonna |
Back court |
14.7 |
4.4 |
9.3 |
40.3 |
|
8.2 |
| 2. Darrell Boars |
Front court |
12.6 |
10.6 |
2.1 |
34.5 |
|
6.5 |
| 3. Silk Curry |
Back court |
13.5 |
8.7 |
1.7 |
29.3 |
|
5.2 |
| 4. Romon Dion |
Back court |
27.1 |
7.1 |
4.5 |
42.5 |
|
16.4 |
| 5. Joe Eastcoast |
Back court |
18.1 |
7.5 |
5.1 |
41 |
|
14.3 |
| 6. Abdul Famous |
Front court |
22.8 |
9.5 |
2.4 |
38.5 |
|
23.5 |
| 7. Hiram Grant |
Front court |
9.3 |
12.2 |
3.5 |
31.5 |
|
4.7 |
| 8. Antoine Roadman |
Front court |
10.2 |
12.6 |
1.8 |
44.4 |
|
7.1 |
| 9. Fred Westcoast |
Front court |
16.9 |
2.5 |
11.4 |
42.7 |
|
15.8 |
| 10. Magic Jordan |
Back court |
28.5 |
6.5 |
1.3 |
38.1 |
|
26.4 |
| 11. Barry Bird |
Front court |
24.8 |
8.6 |
6.9 |
42.6 |
|
19.5 |
| 12. Grant Hall |
Front court |
11.3 |
12.5 |
3.2 |
39.5 |
|
8.6 |