Problem 2: (20 points each for a total of 60 points) The Texas Electronic 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 available scientists (40) and the budget available for projects ($300,000). Following are the re- source requirements and the estimated profit for each project. Project 120 82 1 2 3 4 5 6 7 8 Expense Scientists Profit ($000) Required ($000) 80 7 36 9 145 8 29 133 3 98 50 5 17 75 7 20 88 9 41 100 6 48 Table 2: For Problem 1. 1. What is the maximum profit, and which projects should be selected? 2. Suppose that management decides that projects 2 and 4 are mutually exclusive. What are the revised project portfolio and (maximum) profit? 3. Suppose that management also decides to undertake at least two of the projects involving consumer products (i.e. two of projects 5 to 8). What are the revised project portfolio and (maximum) profit