## 1 Introduction  
Carotenoids are a group of natural pigments that are commonly found in nature. Because of their well-documented health effects, researchers are continually looking for new methods to obtain these compounds. Chemical synthesis processes provide a substantial proportion of carotenoids for industrial applications. However, as the need for natural dyes continues to rise, the production of these compounds with the use of microorganisms is becoming increasingly important [1, 2]. Among the microbes that can produce carotenoids, yeasts of the _Rhodotorula_ genus are particularly interesting. The major carotenoids synthesized by these organisms are \(\beta\)-carotene, torulene, and torularhodin [3]. Beta-carotene is the most potent precursor of vitamin A and possesses strong antioxidant properties, and hence has a number of health benefits, such as reducing the risk of diseases and certain types of cancer, protecting against macular degeneration, and strengthening the immune system. It is used as a dye and an ingredient of dietary supplements in the food industry, while in the cosmetic industry, it is applied as an ingredient in sun creams [4]. Torulene, a caroten containing 13 double bonds, exhibits pro-vitamin A and anticancer properties. It has an intense orange color and is indicated as a potential food additive [5]. However, torulene production is not carried out on a large scale because the exact pathway of its biosynthesis and the optimal cultivation conditions are unknown [5,6]. Torularhodin belongs to the group of xanthophyls, and, depending on the concentration, its color ranges from pink to orange [5]. It can be used in medicine, for example, for the prevention of prostate cancer or in pharmaceuticals, which is associated with the apoptosis of neoplastic cells (reduction of Bcl-2 proteins and increased expression of Bax protein and specific caspases [7]. Furthermore, it possesses strong antimicrobial properties and, therefore, can be used as a natural antibiotic [8].  
The selection of appropriate strains that can synthesize higher amounts of these compounds, as well as optimization of culture conditions, is essential for the profitable production of carotenoids using microorganisms. Several factors influence the process of carotenoid biosynthesis, of which the most important are carbon and nitrogen source, pH, oxygenation level, and availability of light [2]. Various agri-food wastes have been used for production to reduce the costs of microbiological media. It was shown that glycerol, a by-product of the biodiesel production process, can be successfully used as a carbon source, and potato wastewater, obtained in large amounts from potato starch production, as a nitrogen source [9]. The presence of appropriate micronutrients in the culture medium is also necessary to achieve high yields of carotenoids [10], as these compounds act as cofactors of cellular enzymes involved in their biosynthesis. For example, Mg\({}^{2+}\) or Mn\({}^{2+}\) ions act as cofactors of phytoene synthase, and Fe\({}^{2+}\) ions ensure the proper activity of \(\beta\)-lycopene cyclase [3]. The presence of some metals may also be an environmental stress factor for yeast cells, inducing increased carotenogenesis [11]. Another factor that influences carotenoid biosynthesis in red yeast cells is the presence of vitamins. Among vitamins, B group plays an important role in yeast metabolism [12, 13, 14, 15]. However, no studies have analyzed the effect of these vitamins on the biosynthesis of carotenoids by _Rhodorula_ yeasts so far. Therefore, this study aimed to investigate the effect of supplementation of the culture medium prepared from two types of industrial wastes (glycerol and potato wastewater) with selected cations and B vitamins on the biosynthetic efficiency of _Rhodorula muclaginous_ as well as the profile of carotenoids produced by this yeast species.