A frequently voiced critique is that due to lower yields on organically managed farmlands, one cannot feed a country using organic agriculture. In this paper, we aim to mathematically disprove this claim by developing a linear programming model and produce a detailed agriculture plan for Turkey sufficient to feed her population with a 2400 kcal daily menu on average, solely comprising of organic foods. The model uses information about population sizes and food needs of 81 cities in Turkey, and yields of 120 food, feed, forage crops, and four animal products. Intensive and extensive livestock production methods as well as food transportation between cities has been incorporated into the model. The resulting problem with 950 thousand variables and 40 thousand constraints can be solved with an optimization package in under a minute. Results, prescribing how many acres of each crop should be grown in each city, indicate that to feed the country fully on organic produce, 63% of the arable land suffices, yielding 8.9 million hectares of unused land where further organic foods could be grown for export or aid. We also run the model under different scenarios: fully vegetarian diet, omnivore model, different transportation structures, drought conditions and a limit on fruit trees. With this work, we have shown that it is possible to feed the whole population of Turkey with an agricultural practice that is not harmful to human health, soil, water and air; respects biological cycles and reduces food miles and fossil fuel consumption, thus contributing to sustainability and fighting climate change. We tested preliminary scenarios to understand the robustness of organic agriculture in the face of extreme weather events. The proposed model can also be applied to other countries when appropriate data are used.