This article tries to discuss profit maximization policies by using four variable inputs, such as capital, labor, principal raw materials, and other inputs in an industry, where mathematical economic models are applied by considering budget constraint. For the sustainable production, every industry should apply scientific method, such as mathematical techniques to obtain more accurate results. In the study Cobb-Douglas production function is analyzed with detail mathematical analysis. The sensitivity analysis is included in the operation to show profit maximization that is a pivotal goal of the industry. The economic predictions of future production are provided through the comparative statics to become sure of profit maximization before starting of production in the industry. In the study Lagrange multiplier technique is applied to achieve optimal result in every step of industrial operation.

Grounded theory (GT) is a general research method that provides the efficient generation of theory from data, which are collected by a strong, sound, and fair research method. It is an inductive methodology that systematically collects and analyzes data for developing theory on human behavior in social welfare perspectives. It is considered as one of the most popular qualitative research methodologies in the world. It is originally developed by two American sociologists Barney Galland Glaser and Anselm Leonard Strauss in 1967 through the publication of their revolutionary book The Discovery of Grounded Theory. It emphasizes the importance of developing an understanding of human behavior through a process of discovery. Grounded theory has originated in sociology, and at present it has become a key methodological setting in a wide range of other disciplines, such as in nursing, physiotherapy, healthcare, education, anthropology, psychology, management, information systems, software engineering, etc. It is useful both for expert and novice researchers to generate new explanatory theories. This article tries to discuss grounded theory methodology through the discussion of its origin and development, basic principles, characteristics, advantages and disadvantages, and its usefulness in social science researches for qualitative analysis.

This article tries to explore the constructivist grounded theory (CGT) in qualitative research. American sociologist Kathy Charmaz has developed a new qualitative research field “Constructivist Grounded Theory” for the first time in 2006. Constructivist grounded theory is a qualitative research methodology that draws comparison between the ethical principles of deontology, utilitarian and virtue ethics, and individuals seek to understand the world in which they live and work. It is a popular method for research studies mainly in psychology, education, and nursing. In social sciences, it represents culture, context, literacy, personal experiences, as well as application of knowledge. It also presents the theoretical substructures of symbolic interactionism and constructivism. Constructivism is used for research, learning, and teaching with peers. There are various types of constructivism, such as social, psychological, personal, radical, and contextual constructivism. On the other hand, symbolic interactionism is the process of human interaction that provides the meanings for the experiences through language, symbols, and social interactions. This study tries to investigate how constructivist grounded theory has developed in times from the original grounded theory of Glaser and Strauss. The paper also tries to highlight characteristics, application, and importance of constructivist grounded theory.

In the society utility is the vital concept, especially in mathematical economics. It is considered as the tendency of an object or action that increases or decreases overall happiness. In social sciences, the property of a commodity that enables to satisfy human wants is called utility. This paper has tried to operate utility maximization policy of an organization by considering two constraints: budget constraint and coupon constraint. To develop the maximization policy of utility function, the techniques of multivariate calculus are used. In this study four commodity variables are used to operate the mathematical analysis efficiently. In this article Lagrange multiplier technique is applied to achieve optimal result throughout the study.

In mathematical economics utility is the vital concept. In the society utility is considered as the tendency of an object or action that increases or decreases overall happiness. This study tries to discuss sensitivity analysis during utility maximization investigation. Actually, the method of Lagrange multipliers is a very useful and powerful technique in multivariable calculus. In this paper mathematical formulation of Lagrange multipliers is derived through the optimal devise. This article has taken attempts to find relations among commodities and coupons when the prices of different commodities increase or decrease.