[Chapter 12] Integer Linear Optimization Models The Highland Investment Group is considering investing in four projects. The expected net present value (NPV) and the required capital at the present time for each project are given in the table below. Project Expected NPV ($) 1 10,000 Required Capital ($) 3,000 5,000 2.000 2 16,000 3 6,000 4 9,000 4,000 At present a budget of $12,000 is available for investment. Highland has specific requirements for the investment, as detailed in the Constraints section given below. Please help Highland develop an investment plan by formulating an integer linear optimization model. Write your final answer only (without intermediate steps) for the fill-in-the-blank questions 1. Define the decision variables. (Note: This step is done for you. Please use these decision variables hereafter.) Xi = 1 if project 1 is selected for investment otherwise, X2 = 1 if project 2 is selected for investment: 0 otherwise, X; - 1 if project 3 is selected for investment: 0 otherwise X4 - 1 if project 4 is selected for investment; otherwise, II. Write the objective (mathematically). a * 99 Question 17 (2 points) Saved At least two projects must be selected. OX1 + X2 + X3 + X4 3 2 X1 + X2 + X3 + X4 = 2 O X1 + X2 +Xg+X4 2 2 X1 + X2 + X3+X4 > 2 OX1 + X2 + X3 + X4