Extruded snacks are commonly made with cereals with good expansion properties but low in essential nutrients such as protein and vitamins. The incorporation of legume and vegetable crops into cereal improves the nutritional value of cereal-based extruded snacks. This study aimed to develop a nutrient-rich optimized extruded snack by incorporating orange-fleshed sweet potato, finger millet, and soybean flour. The extrusion processing conditions were barrel temperature (90–130 °C) and feed moisture content (20–26%). Thirteen treatment combinations were generated for this experiment using a face-centered central composite design. Standard methods were used to evaluate the effect of barrel temperature and feed moisture content on extruded snacks' nutritional, anti-nutritional, physical, functional, and sensory acceptability. The data were analyzed, and processing conditions were optimized using the response surface methodology of Design Expert software version 13. Multiple regression analysis showed significant effects (p < 0.05) of the independent variables on moisture, protein, fat, beta-carotene, bulk density (BD), hardness, expansion ratio (ER), water absorption index (WAI), water solubility index (WSI), and overall acceptability of the extrudates. The optimum response of 14.06% protein, 3.26% ash, 69.12% carbohydrate, 6.477 mg/100 g beta-carotene, 0.36 g/ml bulk density, 2.72 Expansion ratio, 87.28 N hardness, 4.34 g/g Water absorption index, 22.34% Water solubility index, and overall acceptability of 3.30 was achieved at an optimal barrel temperature of 114.5 °C and feed moisture content of 20%. The obtained result suggests that barrel temperature and feed moisture content had a significant influence (p < 0.05) on the measured quality properties of the extrudates.
