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 resource requirements and the estimated profit for each project:

Project Expense ($1,000s) Management Scientists Estimated Profitt
Required ($1,000,000s)
1 $60 7 $0.36
2 110 9 0.82
3 53 8 0.29
4 47 4 0.16
5 92 7 0.56
6 85 6 0.61
7 73 8 0.48
8 65 5 0.41

Required:
Formulate the integer programming model for this problem and solve it by using the computer.