Question 1: Integer Programming (25 Points) 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 Management Estimated Profit ($1,000s) Scientists Required ($1,000,000s) 1 $ 60 7 $0.36 100 9 0.82 N 3 53 8 0.29 4 47 4 0.16 5 92 7 0.56 6 85 6 0.61 7 8 0.48 73 65 8 5 0.41 a. Define the decision variables. (3 Points) b. Develop the objective function. (3 Points) c. Write the constraints. (9 Points) d. Solve the problem in Excel. (10 Points: Decision variables section: 1 points, O.F. Section: 1 points, Constraints section: 3 points, Solver: 5 points)