#3) (50 points) A company is planning to start k new projects out of the project proposals. The selected projects must be started and finished within the next T months. Each project has an associated benefit denoted by bl. The overall cost of completing the project is given by er and the budget the company allocated for the selected projects is C. To start project i requires a set up time si given in months and the number of months required to complete project is given by d. There are some restrictions in terms of which projects can be selected. Project 1 and 2 cannot be selected together. If project 3 is selected, then first project 4 and then project 5 must be completed before project 3 can be started. A project can be started at most once during the given T months and must be completed within the time horizon of T months. Formulate this problem so that the overall benefit for the company is maximized. #3) (50 points) A company is planning to start k new projects out of the project proposals. The selected projects must be started and finished within the next T months. Each project has an associated benefit denoted by bl. The overall cost of completing the project is given by er and the budget the company allocated for the selected projects is C. To start project i requires a set up time si given in months and the number of months required to complete project is given by d. There are some restrictions in terms of which projects can be selected. Project 1 and 2 cannot be selected together. If project 3 is selected, then first project 4 and then project 5 must be completed before project 3 can be started. A project can be started at most once during the given T months and must be completed within the time horizon of T months. Formulate this problem so that the overall benefit for the company is maximized