[Chapter 13] Integer Linear Optimization Models The Emecald imvestment Group is considering investing in six projocts. The expected net present value (NPY) and the required capital at the present time for each profect are given in the table below. At pretent, a budget of 521,000 is avaiable for imetment. Emerald has specific requiremitnts for the investment as dealaied in the Contralnts section kiven below. Please helo Emerald devilop an inveitment olan by formulating an ioteser lines. optimitation model. 1. Define the decision variables (Note: This step b done for you. Please use these decision variables hereafter.) X1=1 if project 1 is selected far imvestment: Q othervise. X2=1 if project 2 is selected for imvestment 0 otherwise. X9=1 if project 3 is selected for imvestment 0 otherwise. x4=1 if project 4 is selected for imvestment: 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 in the obinctive? Mnz=5,000x1+7,000x2+2,000x2+4000x4+6000x3+3,000x8Mnz=x1+x2+x2+x4+x5+x2Maxz=5000x1+7,000x2+2000x3+4000x4+6000x1+3000x4Man2=6,000x1+1.000x2+1.000x3+5,000x4+7000x3+4000x6Marz+x3+x2+x2+x1+x1+x2Menz+6000x1+a,000x7+3,000x3+5000x1+7000x3+4000x4 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