Optimizing microgrids with renewable sources is a challenging due to high initial costs, operational constraints, and uncertain generation. This paper presents a resource-efficient stochastic optimization method based on interior-point method (IPM). The approach is applied for optimal sizing and dispatch of distributed energy resources and storage in microgrids. To address this, a nonlinear cost-based model with two-stage optimization is formulated under varying renewable penetration and reliability levels. Uncertainties in solar, wind, and demand are modeled using beta distribution. Results show that a renewable penetration of 55% reduces the carbon emissions by 42.2% with only an 8.53% cost increase.