Formulate an integer program for following table
Hagger Engineering Corporation is considering undertaking several proposed projects for the next fiscal year. The projects, the number of engineers and the number of support personnel necessary for each project, and the expected profits for each project are summarized in the following table:
|
|
Project
|
|
|
1
|
2
|
3
|
4
|
5
|
6
|
|
Engineers Required
|
20
|
55
|
47
|
38
|
90
|
63
|
|
Support Personnel Required
|
15
|
45
|
50
|
40
|
70
|
70
|
|
Profit (million $)
|
2.0
|
3.6
|
4.0
|
3.0
|
7.2
|
4.4
|
Formulate an integer program that maximizes Hagger's profit subject to the following management constraints:
(a) Classify variables
(b) Use no more than 175 engineers
(c) Use no more than 150 support personnel
(d) If either project 6 or project 4 is done, both must be done
(e) Project 2 can be completed only if project 1 is done
(f) If project 5 is completed, project 3 must not be done and vice versa
(g) No more than three projects are to be done.