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

**Please show your steps in your work.

14. The Texas Consolidated Electronics Company is contemplating a research and development pro- gram 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 Required Estimated Profit ($1,000,000s) 1 $ 60 110 7 9 2 3 $0.36 0.82 0.29 0.16 3 53 8 4 4 47 5 7 0.56 6 92 85 73 6 0.61 0.48 7 8 8 65 5 5 0.41