Make a spreadsheet model and solve. Include a textbox with the ILP formulation and a separate one for the optimal solution and optimal vale. For parts c and d, do not include your answer with the original formulation or solving the problem.

5. BeFair Corporation has $30 million to allocate to the various projects of its three subsidiaries for the next year. BeFair has established that at least one project from each subsidiary must be funded. The profit (return investment) at the end of the year and the required investments are given in the table below for each project, where projects 1 to 3 belong to sub- sidiary 1, projects 4 to 6 belong to subsidiary 2, and the rest belong to subsidiary 3. PROJECT PROFIT (IN MILLION $) INVESTMENT (IN MILLION $) 1 0.50 2 2 1.40 5 3 1.70 12 4 1.10 2 5 4.00 15 6 0.60 3 7 2.50 10 8 1.10 1 BeFair wants to decide which projects to fund so that the total profit will be max- imized. Formulate this problem in the space provided on the answer sheet. a. Clearly define the decision variables you would use to solve this problem. b. Formulate an integer linear program for the above problem using only the decision variables defined in a. c. Formulate the following constraint: BeFair decided to fund at most 2 projects of subsidiary 2. d. Formulate the following constraint: Project 1 cannot be funded unless projects 4 and 5 are also funded. 5. BeFair Corporation has $30 million to allocate to the various projects of its three subsidiaries for the next year. BeFair has established that at least one project from each subsidiary must be funded. The profit (return investment) at the end of the year and the required investments are given in the table below for each project, where projects 1 to 3 belong to sub- sidiary 1, projects 4 to 6 belong to subsidiary 2, and the rest belong to subsidiary 3. PROJECT PROFIT (IN MILLION $) INVESTMENT (IN MILLION $) 1 0.50 2 2 1.40 5 3 1.70 12 4 1.10 2 5 4.00 15 6 0.60 3 7 2.50 10 8 1.10 1 BeFair wants to decide which projects to fund so that the total profit will be max- imized. Formulate this problem in the space provided on the answer sheet. a. Clearly define the decision variables you would use to solve this problem. b. Formulate an integer linear program for the above problem using only the decision variables defined in a. c. Formulate the following constraint: BeFair decided to fund at most 2 projects of subsidiary 2. d. Formulate the following constraint: Project 1 cannot be funded unless projects 4 and 5 are also funded