[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. At present, a budget of $21,000 is available for investment. Emerald has specific requirements for the investment, as detailed in the Constraints section given below. Please help Emerald develop an investment plan by formulating an integer linear optimization model. I. 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=1 if project 5 is selected for investment; 0 otherwise. X6=1 if project 6 is selected for investment; 0 otherwise. What is the objective? MinZ=5,000X1+7,000X2+2,000X3+4,000X4+6,000X5+3,000X6 MinZ=X1+X2+X3+X4+X5+X6 MaxZ=5,000X1+7,000X2+2,000X3+4,000X4+6,000X5+3,000X6 MaxZ=6,000X1+8,000X2+3,000X3+5,000X4+7,000X5+4,000X6 MaxZ=X1+X2+X3+X4+X5+X6 MinZ=6,000X1+8,000X2+3,000X3+5,000X4+7,000X5+4,000X6 Among projects 1,3 , and 4 , two of them must be selected. X1+X3+X4>2X1+X2+X3+X4+X5+X6=2X1+X3+X4=2X1+X3+X4