You have built an integer programming $($IP$)$ model to minimize total costs for a logistics distribution problem. After solving the model using Excel Solver, you find the optimal total cost is $$500,000,$ with all decision variables constrained to be integers $($e$.$g$.,$ number of trucks, warehouses, etc.$).$

To explore efficiency, you decide to remove the integer constraints and solve the same model as a Linear Programming $($LP$)$ relaxation.