One of the issues of the Civil Construction Industry is around the planning phase of the the project, when is possible to verify the difficulty in completing the project in time, initially, thinking as the contractor. Therefore, the present study proposes the application of the linear programming method as a solution to the problem of the optimization of the factors time and costs from the Civil Construction projects. Initially it was done, by bibliographic mapping, also as the re-reading of some basic concepts, programming Technics with network and critical path. Afterword, it was discussed definitions of operational research and mathematical models of Linear Programming. It was proposed, therefore, a method aiming the solution of the issue of the time optimization and projects expenses of Civil Construction. To demonstrate the application of the proposed method, it was used as a scenario, a governmental construction project, that the goal was the compression of the project in 14 days, reaching a period of contract, a cost of compression the amount of R$ 95,040.15 (ninety five thousand forty dollars and fifteen cents), less than if there were an increase in penalty for delay. With this achieved our objective, i.e., compression project for the desired duration.
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