A real estate development firm, Peterson and Johnson, is considering five possible development projects. The following table shows the estimated long-run profit (net present value) that each project would generate, as well as the amount of investment required to undertake the project, in units of millions of dollars. The owners of the firm, Dave Peterson and Ron Johnson, have raised $20 million of investment capital for these projects. Dave and Ron now want to select the combination of projects that will maximize their total estimated long-run profit (net present value) without investing more that $20 million. Mathematically formulate a binary programming model for the above problem. To do so, define your decision variables clearly, and clearly write the objective function and the constraints. Mathematically formulate the following restrictions as linear constraints independent of each other and the above capital restriction. If project 1 is selected, then project 2 cannot be selected. If project 3 is selected, then project 4 has to be selected. At most four projects can be selected. At least two projects should be selected. If project 5 is selected, then at most two other projects can be selected. If project 4 is selected, then at least two other projects should be selected. Project 3 cannot be the only project selected. If both projects 2 and 3 are selected, then project 5 cannot be selected. If both projects 4 and 5 are selected, then project 1 has to be selected. If both projects 1 and 2 are selected, then at most one other project can be selected. Mathematically formulate the following restrictions as linear constraints independent of each other and the above restrictions. Note, in some of them, you might need to define additional variables. The total spending on the project selections should be EITHER less than or equal to $10 million OR greater than or equal to $15 million. If you select some projects, you need to select at least two projects