2:00:00 3 Formulate (set up) the linear programming model for the following problem. Be sure to clearly define the decision variables, objective function and indicate all restrictions related to the decision variables. A private equity firm is considering five competing projects in which to invest in the upcoming quarter. The firm needs to decide how to allocate its available capital based upon the combination of projects (denoted as projects 1-5 below) selected to maximize returns (based upon net present value (NPV)). Table 1 below presents the capital requirements and the NPV for each project, along with the associated risk (given as a percentage of the initial investment). The company has $48 million in capital to allocate, with the goal of having an average associated risk of no more than 5.8%. There are some additional constraints to be met: (1) if project 2 is selected, then project 4 is also selected; (ii) one of project 1 or project 3 must be selected, but not both; (iii) at least one of projects 2, 3, or 5 is selected Table 1: Project Data 9 Project NPV (SM) Risk (%) Capital (SM) 1 21 4.6 14 12 2 19 5.4 11 3 26 7.3 13 st 15 4 22 5.9 12 23 5.2 16 18