[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. 1 2 3 4 Project Expected NPV ($) Required Capital ($) 10,000 3,000 16,000 5,000 6,000 2.000 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.) Xz = 1 if project 1 is selected for investment: 0 otherwise. X2 = 1 if project 2 is selected for investment: 0 otherwise X3 .1 it project 3 is selected for investment: 0 otherwise. X4 - 1 if project 4 is selected for investment: 0 otherwise Il Wirita thabiti Question 15 (2 points) Constraint on the budget. 10,000 X2 + 16,000 X2 + 6,000 X3 + 9,000 X4 5 12,000 OX1 + X2 + X3 + X4 $ 12,000 3,000 X1 + 5,000 X2 + 2,000 X3 + 4,000 X4 - 12,000 3,000 X1 +5.000 X2 + 2,000 Xy + 4,000 X4 $ 12,000 3,000 X1 +5.000 X2 + 2.000 X3 +4,000 X42 12,006 1 Question 16 (2 points) If project 2 is selected, project 4 cannot be selected. OX22X X2+ X431 OX, X X2 + X=1 X2+X41