The question of how to minimize monetary cost while meeting basic nutrient requirements (a subsistence diet) was posed by George Stigler in 1945. The problem, known as Stigler's diet problem, was famously solved using the simplex algorithm. Today, we are not only concerned with the monetary cost of food, but also the environmental cost. Efforts to quantify environmental impacts led to the development of footprint (FP) indicators. The environmental footprints of food production span multiple dimensions, including greenhouse gas emissions (carbon footprint), nitrogen release (nitrogen footprint), water use (blue and green water footprint) and land use (land footprint), and a diet minimizing one of these impacts could result in higher impacts in another dimension. In this study based on nutritional and population data for the United States, we identify diets that minimize each of these four footprints subject to nutrient constraints. We then calculate tradeoffs by taking the composition of each footprint's minimum diet and calculating the other three footprints. We find that diets for the minimized footprints tend to be similar for the four footprints, suggesting there are generally synergies, rather than tradeoffs, among low footprint diets. Plant-based food and seafood (fish and other aquatic foods) commonly appear in minimized diets and tend to most efficiently supply macronutrients and micronutrients, respectively. Livestock products rarely appear in minimized diets, suggesting these foods tend to be less efficient from an environmental perspective, even when nutrient content is considered. The results' emphasis on seafood is complicated by the environmental impacts of aquaculture versus capture fisheries, increasing in aquaculture, and shifting compositions of aquaculture feeds. While this analysis does not make specific diet recommendations, our approach demonstrates potential environmental synergies of plant- and seafood-based diets. As a result, this study provides a useful tool for decision-makers in linking human nutrition and environmental impacts.
