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Packaging produced from renewable resources and agricultural coproducts offers opportunities to advance circular economy strategies and reduce dependence on fossil-based materials. Quinoa stems can be incorporated into starch-rich matrices from Andean tubers, providing an alternative use for agricultural biomass. Characterizing extractable phenolic compounds in these materials can support their valorization and guide further investigation of packaging functionality. This study optimized the solvent composition and number of extraction cycles for recovering total soluble phenolic compounds (TSPC) from biodegradable trays formulated with 45% whole oca flour, 45% whole yellow mashua flour, and 10% quinoa stem flour. Trays were manufactured by thermoplastic extrusion using a seven-zone temperature profile of 30, 55, 80, 105, 110, 105, and 90 °C, followed by thermoforming at upper and lower platen temperatures of 130 and 120 °C, respectively, for 8 min. Extraction was assisted by low-frequency ultrasound operating at 40 kHz and 100 W. A four-component simplex-centroid mixture design evaluated water, methanol, ethanol, and acetone as independent variables. The matrix comprised four pure solvents, six binary mixtures, four ternary mixtures, four formulations enriched in one component, and four replicates of the equimolar mixture, totaling 22 trials. Absorbance at 750 nm, determined using the Folin–Ciocalteu method, was the response variable. Response surface methodology (P < 0.10; R2 > 0.85) and desirability analysis were used to optimize solvent composition. Experimental absorbance ranged from 0.089 to 0.880. Among pure solvents, water yielded the highest response (0.405), followed by methanol (0.376), ethanol (0.119), and acetone (0.089). The equal-proportion water–methanol mixture increased absorbance to 0.755, whereas the methanol–ethanol mixture yielded 0.201. The highest experimental response was obtained with equal proportions of water, methanol, and acetone (0.880), followed by the water–methanol–ethanol mixture (0.822). These differences demonstrate the importance of solvent composition for recovering compounds from the thermomechanically processed matrix. The selected model explained 90.24% of response variability, with an adjusted coefficient of determination of 0.854. Optimization identified a formulation containing 50% water and 50% methanol, acidified with 1% HCl, with a predicted absorbance of 0.8526 and a desirability of 0.9651. Experimental validation showed a relative deviation of 5% between observed and predicted responses, supporting model adequacy at the optimized composition. Subsequently, the number of successive extraction cycles was optimized, and six cycles were required to recover 95% of TSPC. This endpoint provided satisfactory recovery while limiting additional solvent consumption and processing effort. Overall, the validated ultrasound-assisted procedure established suitable conditions for phenolic characterization of trays containing Andean tubers and quinoa stems. Incorporating agricultural coproducts into renewable packaging supports circular material use, while the optimized analytical protocol provides a basis for further assessment of these materials and their potential contribution to more sustainable packaging systems.
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