[Chapter 12] Integer Linear Optimization Models Sunrise Investment Group is considering investing in six new projects. The required capital at the present time and the expected net present value (NPV) for each project are given in the table below 1 Project Required Capital ($) Expected NPV ($) 3,000 10,000 2 5,000 16.000 3 2,000 6,000 4 4.000 9.000 5 7.000 20,000 6 6.000 18.000 At present, a budget of $20,000 is available for investment. Sunrise has some specific requirements (as detailed in the Constraints section below). Please help Sunrise develop an investment plan by formulating an integer linear optimization model. Follow the steps below. 1. Define the decision variables I. Define the decision variables. (Note: This step is done for you. pilase use these decision variables hereafter.) X1 = 1 if project 1 is selected for investment: 0 otherwise. X2 = 1 if project 2 is selected for investment: O otherwise. X3 = 1 if project 3 is selected for investment 0 otherwise. X4 = 1 if project 4 is selected for investment. O otherwise. X3 = 1 if project 5 is selected for investment: 0 otherwise. Xo = 1 if project 6 is selected for investment: 0 otherwise. Question 40 (2 points) This is a problem. minimization maximization Question 41 (2 points) The objective function is (3,000 (10,000) X1 (5,000|(16,000) X2 + (2.000/(6.000X3 + (4.000X9.000) X. + (7,000M20,000) Xs+ (6.000X18.000) X X + X2 + X3 + X+X5 + X 10,000 X: + 16.000 X2 + 6,000 X3 + 9.000 X4 +20,000 Xs + 18,000 X b 3,000 X, 5.000 X2 + 2,000 X3 + 4,000 X4+ 7.000 Xs +6,000 X Question 42 (4 points) Constraint on the budget (3,000)(10,000) X, +(5,000X16,000) X2 + (2.000)(6,000) X3 + (4,000)9,000) X4 +(7.000X20,000) Xs +(6,000)(18,000) X6 $ 20,000 3,000 X1 + 5,000 X2 + 2,000 X3 +4,000 X4 + 7,000 X5 +6,000 X $ 20,000 X1 + X2 + Xg+ X4+ X5 + Xo 220.000 10,000 X1 + 16,000 X2 + 6,000 X3 + 9,000 X4+20,000 Xs + 18,000 X6 ? 20,000 OX + X + X3 Xs+ Xo $20,000 10.000 X: + 16,000 X2 + 6,000 X3 + 9.000 X + 20,000 Xs + 18,000 X 5 20.000 3,000 X, +5,000 X, 2.000 Xy+4.000 X4 + 7,000 Xs + 6,000 X 220,000 (3.000 10.000) X+(5.000)(16,000) X2 + 2,000)(6,000) X3 + 14,000)(9.000) X4 + (7.000 20.000) Xs +(6,000x18.000) X 2 20,000 Question 43 (4 points) At least three projects must be selected. O X + X + Xz+ + Xg+Xq> 3 OX + X2 -Xg+ Xg 23 OX + X2 + -Xg+ X 1 OX - Xg X = X