The Texas Consolidated Electronics Company is contemplating a research and development program encompassing eight research projects. The company is constrained from embarking on all projects by the number of available management scientists (40) and the budget available for R&D projects ($300,000). Further, if project 2 is selected, project 5 must also be selected (but not vice versa). Following are the resources requirement and the estimated profit for each project.
| Project |
expenses $1,000
| scientists required |
profit (1,000,000)
|
| 1 |
50 |
6 |
0.30 |
| 2 |
105 |
8 |
0.85 |
| 3 |
56 |
9 |
0.20 |
| 4 |
45 |
3 |
0.15 |
| 5 |
90 |
7 |
0.50 |
| 6 |
80 |
5 |
0.45 |
| 7 |
78 |
8 |
0.55 |
| 8 |
60 |
5 |
0.40 |
Formulate the integer programming model for this problem and solve it using the computer.