A company needs to choose from four potential projects to undertake, where each project would run for 3 years and have the following characteristics: Project Return (Em) 1 2 3 0.2 0.3 0.5 0.1 4 Available capital (Em) Capital requirements (Em) Year 2 Year 1 Year 3 0.5 1.0 1.5 0.1 3.1 0.3 0.8 1.5 0.4 2.5 0.2 0.2 0.3 0.1 0.4 That is, project 1 would give a return of 0.2m and require the company to invest 0.5m of its capital in the 1st year, 0.3m in the second year and 0.2m in the 3rd year. The capital available for investing in the projects in each year is given in the table above. The company needs to decide which projects to choose in order to maximise the total return, while satisfying budgetary constraints in each year. 1. Formulate this problem: define decision variables and mention what each of them represent, formulate the objective function and all necessary constraints. 2. Solve with LPSolve (include .lp file). 3. How much of its capital has the company underspent in each year under this solution? 4. Suppose now that we have the additional condition that either project 3 or project 4 can be chosen (i.e., projects 3 and 4 are mutually exclusive). (a) How will your formulation change? (b) How will the optimal solution change, if at all? (c) How will the amount of underspent capital in each year change?