Part 4: Integer Linear Optimization Model The Sunrise Investment Company is considering investing in four projects. The expected net present value (NPV) and the required capital at the present time for project are given in the table below. Project Expected NPV ($) 12,000 18,000 9,000 10,000 Required Capital ($) 4,000 7,000 3,000 6,000 At present, a budget of $15,000 is available for investment. Sunrise has some specif requirements (as detailed in the constraints section). Please help Sunrise develop an investment plan. Follow the steps below. 1. Define the decision variables. (Note: This step is done for you. Please use these decision variables hereafter.) X1 - 1 if project 1 is selected for investment; O otherwise. Xy - 1 if project 2 is selected for investment: 0 otherwise. X3 - 1 if project 3 is selected for investment; 0 otherwise. X4 - 1 if project 4 is selected for investment; 0 otherwise. Question 33 (2 points) II. Write the objective (mathematically). Max Z- 12,000 X1 + 18,000 X2 + 9,000 X3 + 10,000 X4 Max Z-4,000 X1 +7,000 X2 +3,000 X3 + 6,000 X4 Min Z - 12,000 X1 +18,000 X2 + 9,000 X3 + 10,000 X4 OX1 + X2 + X3 + X4 s 15,000 Question 37 (2 points) At most three projects are to be selected. X1 + X2 + X3 3 3 X1 + X2 + X3 + X4 s 3 X1 + X2 + X3 2 3 OX1 + X2 + X3 + X4 2 3 Question 38 (2 points) If project 1 is selected, project 4 cannot be selected. OX1 + X451 OX1 + X4 2 1 OX1 X4 OXZX4 Question 39 (2 points) Saved