[Chapter 13] Integer Linear Optimization Models The Emerald Investment Group is considering investing in six 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. 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; 0 otherwise. X2=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. X5 i 1 if project 5 is selected for investment; 0 otherwise. X6=1 if project 6 is selected for investment; 0 otherwise. Question 14 (2 points) Saved What is the objective? Maxz=x1+x2+x3+x4+x5+x6 MaxZ=5,000x1+7,000x2+2,000x3+4,000x4+6,000x5+3,000x6 Max Z=6,000X1+8,000X2+3,000X3+5,000X4+7,000X5+4,000X6 Min Z=6,000X1+8,000X2+3,000X3+5,000X4+7,000X5+4,000X6 Min z=x1+x2+x3+x4+x5+x6 Min z=5,000x1+7,000x2+2,000x3+4,000x4+6,000x5+3,000x6 III. Write the constraints (mathematically). Among projects 1,3 , and 4 , two of them must be selected. x1+x3+x42x1+x3+x42x1+x2+x3+x4+x5+x6=2 If project 2 is selected, project 5 must be also selected. x2+x51x2>x5x2+x51x2x6x3+x61