Integration of renewable energy and waste heat resources could effectively reduce emissions and the production cost in methane production power plants. The objective of this study is to conduct a technoeconomic analysis of an Iraqi methanol production facility using a combination of energy resources of waste gas from Al-Fallujah white cement factory, solar and wind energy. It is hypothesized that the carbon dioxide present in the flue gas could be extracted using solar and wind turbine energy in a carbon capture unit in the hydrogen plant. Methanol fuel is then produced in the methanol plant from the combined sources. The amount of energy and the number of solar panels or wind turbines (WT) needed to supply this energy requirement were estimated using the Engineering Equation Solver (EES), and then the environmental impact of the methanol plant was assessed. The efficiencies of renewable energy PV, wind turbines, methanol plants, and methanol fuel were predicted as 21%, 35%, 16.26%, and 58.72%, respectively. The electrolyzers' efficiency was 78.2% at their ideal density of 2.2 kA/m$^2$. With a production capacity of 34,530 million tons of methanol, the total cost to operate the plant for 30 years for each of the PV plants and WT was found to be \$9.46 billion and \$5.291 billion, respectively. This translates to 0.4131 \$/kg methane for the PV plant and 0.2413 \$/kg methane for the wind power plant. In terms of the environment, there is a daily 3,894 tons of collected CO$_2$ emissions and 3,306 tons of mitigation. The results show that the current facility can compete with facilities that produce clean synthetic fuel.