You are managing the following project portfolio for a manufacturer. Some projects are nearing completion while some are forecast to last for up to 5 years. Their annual budget forecasts for 2019 2023 are detailed in the table below as are the cumulative net benefits of the projects to the firm. + ID 1 2 3 4 2019 2 10 20 2020 2 10 20 2021 5 8 10 2022 3 10 2023 3 10 8 8 8 5 15 10 1.5 1.5 1.5 Project Factory Logo IT Warehouse Staff Office Canteen Electrical Elevator Tricks Rails Annual Budget Benefits 50 60 70 60 75 5 50 35 65 60 40 23 6 7 8 9 10 11 12 20 20 2.5 2.5 17 2.5 20 15 18 7 17 20 3 4 25 30 25 25 25 Given the interdependencies of several projects and competing objectives of various important stakeholders there are some additional constraints that must be considered. There are some dependency relations that must be followed: Project 1 must be selected with project 4. Project 2 cannot be selected with project 7. Project 9 can only be selected if project 5 is selected. The firm must select one of either project 11 and 12, but not both. a) (15 marks) Formulate a Linear Programming (LP) Model that allow you to select those projects that maximize the benefits of the project portfolio while satisfying all of the dependency and budget constraints. Carefully define your decision variable, objective function and constraints. b) (5 marks) Solve your LP model and interpret the optimal project portfolio. You are managing the following project portfolio for a manufacturer. Some projects are nearing completion while some are forecast to last for up to 5 years. Their annual budget forecasts for 2019 2023 are detailed in the table below as are the cumulative net benefits of the projects to the firm. + ID 1 2 3 4 2019 2 10 20 2020 2 10 20 2021 5 8 10 2022 3 10 2023 3 10 8 8 8 5 15 10 1.5 1.5 1.5 Project Factory Logo IT Warehouse Staff Office Canteen Electrical Elevator Tricks Rails Annual Budget Benefits 50 60 70 60 75 5 50 35 65 60 40 23 6 7 8 9 10 11 12 20 20 2.5 2.5 17 2.5 20 15 18 7 17 20 3 4 25 30 25 25 25 Given the interdependencies of several projects and competing objectives of various important stakeholders there are some additional constraints that must be considered. There are some dependency relations that must be followed: Project 1 must be selected with project 4. Project 2 cannot be selected with project 7. Project 9 can only be selected if project 5 is selected. The firm must select one of either project 11 and 12, but not both. a) (15 marks) Formulate a Linear Programming (LP) Model that allow you to select those projects that maximize the benefits of the project portfolio while satisfying all of the dependency and budget constraints. Carefully define your decision variable, objective function and constraints. b) (5 marks) Solve your LP model and interpret the optimal project portfolio