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The Texas Consolidated Electronics Company is considering an R&D program encompassing eight research projects. In the model for this problem Xi is a 0-1 variable for the selection of project i, where i = 1 to 8. One of the conditions in the model is that the same decision be applied to project 2 and project 5. If project 2 is selected then project 5 is selected. And if project 2 is not selected then project 5 is not selected.  This condition is represented by the following constraint:

Question

The Texas Consolidated Electronics Company is considering an R&D program encompassing eight research projects. In the model for this problem Xi is a 0-1 variable for the selection of project i, where i = 1 to 8. One of the conditions in the model is that the same decision be applied to project 2 and project 5. If project 2 is selected then project 5 is selected. And if project 2 is not selected then project 5 is not selected.  This condition is represented by the following constraint:

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Solution

The condition that the same decision be applied to project 2 and project 5 can be represented by the constraint X2 = X5. This means that if X2 is 1 (project 2 is selected), then X5 is also 1 (project 5 is selected). Similarly, if X2 is 0 (project 2 is not selected), then X5 is also 0 (project 5 is not selected).

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