Problem 1 [30 points): The Texas Electronics Company (TEC) is contemplating an R&D program encompassing eight major projects. The company is constrained from embarking on all projects by the number of scientists (40) and the budget available for projects ($300,000). The following table shows the resource requirements and estimated profit for each project: Project 1 2 3 Scientists Required 7 4 Expense ($000) 60 110 53 47 92 85 73 65 9 8 4 7 6 Profit (5000) 36 82 29 16 56 61 48 41 5 6 7 8 8 5 TEC wants to maximize the total profit from selecting the best projects to embark on. a) Define the decision variables and write down the detailed mathematical formulation of TEC's optimization problem to maximize its total profit. [10 points) b) Solve the optimization problem by Excel Solver. What is the maximum profit, and which projects should be selected? [10 points) c) Suppose the management decides that projects 2 and 5 are mutually exclusive (i.e., TEC should not undertake both). State how you can incorporate this requirement into your model formulation. Solve the revised problem by Excel Solver. What is the 1 revised maximum profit, and which projects should be selected? [10 points)