The Ghanaian population suffers from a double burden of malnutrition. Cost of food is considered a barrier to achieving a health-promoting diet. Food prices were collected in major cities and in rural areas in southern Ghana. Linear programming (LP) was used to calculate nutritionally optimized diets (food baskets (FBs)) for a low-income Ghanaian family of four that fulfilled energy and nutrient recommendations in both rural and urban settings. Calculations included implementing cultural acceptability for families living in extreme and moderate poverty (food budget under USD 1.9 and 3.1 per day respectively). Energy-appropriate FBs minimized for cost, following Food Balance Sheets (FBS), lacked key micronutrients such as iodine, vitamin B12 and iron for the mothers. Nutritionally adequate FBs were achieved in all settings when optimizing for a diet cheaper than USD 3.1. However, when delimiting cost to USD 1.9 in rural areas, wild foods had to be included in order to meet nutritional adequacy. Optimization suggested to reduce roots, tubers and fruits and to increase cereals, vegetables and oil-bearing crops compared with FBS. LP is a useful tool to design culturally acceptable diets at minimum cost for low-income Ghanaian families to help advise national authorities how to overcome the double burden of malnutrition.