## 1 Introduction
However, defining tailored light recipes for specific plant species is not so easy, according to the literature, and other works should consolidate the knowledge in this field. In fact, the optimal light recipe depends not only on the plant species, but also on other factors like the growth stages or the objectives of the growth, e.g., flowering, vegetative growth, fruit, and even postharvest quality management [14; 18]. In addition, environmental variables, such as humidity and temperature, must be taken into strong consideration. Lettuce is ideal for growth in indoor controlled environments thanks to its limited height and short life cycle [19]. There are different studies concerning the effects of light wavelengths on lettuce growth. Blue and red wavelengths are the most common, though light recipes with different blue/red ratios were considered in different studies [20; 21; 22; 23]. Far-red light is beneficial for lettuce when added to red and blue light [24], as it enhances morphological parameters, e.g., fresh weight, dry weight, and leaf area, but also lowers phytochemical concentrations [25]. However, far-red radiation action also depends on the proportion of other wavelengths [26], and its beneficial effect could be stronger if far-red is given alone in the last part of the photoperiod [27]. The effect of green light on lettuce is still not totally clear. According to different studies, its effect seems to be beneficial when added in a limited percentage (10%) to red and blue light, as it enhances the biomass accumulation in lettuce [28; 29], negative if coupled with low blue radiation, and ineffective when coupled with high intensity of blue radiation [30]. However, green light may be useful with plantswith a multilayer canopy, where blue and red lights do not penetrate the surface of the canopy, while green light would go further into the deeper layers of leaves, enhancing their photosynthesis [29,31]. Many factors are involved in the management of VF systems, e.g., the species and cultivar of the crop, the light intensity and wavelength composition, the photoperiod, but also environmental factors and the way nutrients are given to plants [32,33]. Therefore, an optimized and all-embracing management of VF systems must consider the interactions of these factors. This paper attempted to respond to this need, using the Design of Experiments (DoE) methodology. DoE, through a multivariate analysis of variance (ANOVA), is extremely useful for analyzing and modeling the interactions among different variables to build statistical reliable models, as already reported in previous studies [34, 35, 36]. As an innovative part of previous literature, in this work, the growth of baby leaf lettuce (_Lactuca sativa_ L., cultivar Chiara) in an indoor controlled environment was analyzed considering two different light recipes and two categories of slow-release fertilizers in different quantities. Thereafter, both different types of LED lights and fertilizers have been employed as independent variables of the Design of Experiment approach in order to identify and calculate their effect on the response variables. In fact, it is well known that all these parameters can affect plant growth, but a robust statistical approach is almost never applied to perform a quantitative estimation. In addition, the slow-release fertilizers employed in this study have a core-shell structure, where the core is made of porous inorganic material and the shell is made of an organic coating, formulated from waste and by-products compounds, therefore sustainable for the environment. The nutraceutical and morphological properties of lettuce plants were analyzed and mathematically modeled with DoE to understand both the effects of single factors and their interactions. Finally, mathematical models were employed to define a specific optimized condition for the growth of lettuce in a controlled indoor environment, optimizing the use of resources needed specifically for this crop.