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Welcome! In this tutorial Ill formulate linear integer programming models involving Binary or 0-1 variables. Binary variables are employed when there is a yes or no situation. That is, to indicate whether a selection is made or not. For example, suppose we have 4 different projects to consider. We can either select a project, or not select it. So for the first project we can define the decision variable as follows: X1 = 1 if project 1 is selected, and 0 if not selected. We do the same for projects 2, 3, and 4 by defining X2, X3, and X4. Or we can simply write Xi = 1 if project i is selected, and 0 if not selected. where i = 1, 2, 3, and 4. Now, suppose each project has the same lifespan of 3 months (January to March), with corresponding outlays or costs (in thousands of dollars) shown here. Suppose these are the funds available for selected projects each month, and these are the net returns (in thousand dollars) from each project. In this case, our objective is to maximize return whi
