The distribution grid hosting capacity is defined as the amount of new production or consumption that can be added to the grid without adversely impacting the reliability or voltage quality for other customers. In this paper, an optimization-based method for determining the hosting capacity in distribution grids is proposed. The proposed method is developed based on a set of linear power flow equations that enable linear programming formulation of the hosting capacity model. Linearization further helps with determining a near-optimal solution in a short amount of time. The proposed method is examined on a test radial distribution grid to show its effectiveness and acceptable performance. Performance is further measured against existing iterative hosting capacity calculation methods. Results demonstrate that the proposed method outperforms traditional methods in terms of computation time while offering comparable results.