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A three-layer supply chain model with a single supplier, manufacturer, and retailer is presented in this paper. This proposed model is analyzed under green investment along with trade credit and cap-trade policy. It is considered that the manufacturer’s production process is imperfect. Few inferior quality products are reworked, and the remaining defective items are discarded. The manufacturer makes investments in green technology to reduce carbon emissions. The product’s demand is influenced by selling price, advertisement, and green-technology level. The total average profit of the supply chain is constructed under three different scenarios of trade credit provided by the manufacturer to the retailer. The primary goal of this research is to obtain the optimal selling price, production rate, and green-technology level to maximize the system’s total average profit by using genetic algorithm. A numerical example is shown to demonstrate the model, and sensitivity analysis is carried out to analyze the impact of numerous input parameters. Managerial insights and conclusions are provided to make this model helpful for manufacturers.

Calcium ferrite nanoparticles (NPs), doped with Zinc in the range of 10–50mol%, were synthesized through a solution combustion method using citrus Limon extract as a reducing agent, followed by calcination at 500^∘C. The synthesized samples are characterized with different techniques. Bragg reflections confirmed the formation of orthorhombic crystal structure. The shifting of the peak toward higher angle side is observed with increase in the dopant concentration. The surface exhibited irregular shapes and sized NPs with pores and voids in their morphology. The direct energy band gap increases from 2.91 to 2.97eV with increase in Zinc concentration. Further, magnetic and dielectric properties were carried out to know their importance in the high-frequency devices. Magnetic parameters, such as saturation magnetization (M_s), remanence (M_r), and coercivity (H_c) values, are discussed. M_s, M_r and H_c increase with increase in dopant concentration upto 30mol% and thereafter decreases. The dielectric studies revealed a decreasing dielectric constant from 2.98 to 1.84 as the dopant concentration increased. These findings suggest the potential use of these samples in memory devices and high-frequency applications.