International Journal of Engineering Applied Sciences and Technology, 2020 Vol. 5, Issue 3, ISSN No. 2455-2143, Pages 578-581 Published Online July 2020 in IJEAST (http://www.ijeast.com) 578 APPLICATION OF LINEAR PROGRAMMING FOR PROFIT MAXIMIZATION OF A HOUSING CONSTRUCTION COMPANY: A CASE STUDY OF URBANIZATION OF MILLENNIALS Dr. Abhijit Pandit Amity Business School Amity University, Kolkata, West Bengal, India Abstract— The main objective of this paper was to maximize of the profit of a Construction Company in areas of developing a Housing Society and Shopping mall by constructing three types of House (Flat) such as type A (1000 square feet), type B (1200 square feet) and type C (1500 square feet) and shops in mall of type A (100 square feet), type B (180 square feet) and type C (300 square feet) with in constraints such as total number of House (Flat) and shops in the project, material (Concrete, Cement, sand, Glass, etc.) used for each House (Flat) and shops construction, Flooring tiles (stones) used for each House (flat) and shops construction, Colouring used for each House (Flat) and shops and available man Hours. We apply linear programming technique to maximize profit of the company. Keywords— Linear Programming, Model, objective function, Constraints, Decision variables, Maximization. I. INTRODUCTION One of the most important branches of operation research is linear programming. Linear programming is a mathematical technique which contains the strategy of business activities to acquire an optimal solution (Dantzig et al (2006)). It is use for taking decision for optimization of problems that contain many constraints (Dorfman et al (1987)). It is used in many different areas such as in military, health systems, organization, transportation, assignment problems, industries and other real problems for maximum profit. In order to optimize usage of limited resources, the best technique is linear programming (Oladejo et al (2019)). Linear programming technique can be use in many construction plans for optimization. The process to develop a housing society is very complex problem (Wallbaum et al (2012)). Housing development business is a high competition business in construction industry (Arditi et al (2000)). The task to complete the housing construction project within budget and within limited resources is very difficult (Mahdi (2004)). The execution of housing construction project and its management is very challenging. For developing of project there are many important factors such as choice of technology, work definition, estimation of material and duration of project (Hendrickson et al (1987)). Housing construction project is very large-scale project (Kandil et al (2010)). It is used to find minimum construction cost or maximum profit for complete project with condition that total number of house, project time, available materials and number of contractor (Olawale et al (2010)). Many researchers used linear programming in construction business for optimum result such as : (1)Connie et al.(2001) used linear programming for dormitory development plan to calculate number of rooms and area of each facility for maximum profit. (2)Ling (2013) used linear programming technique to find optimal plan for Construction Enterprises. (3)Ahmed (2015) used linear programming technique to find maximum profit within limited budget for a construction project. The objective of this study is to find the maximum profit of a company in the field of development of Housing Society and Shopping Mall. The general form of linear programming problem is Optimize 1 1 2 2 n n z cw cw ... cw     (objective function) …..(1) subject to the constraints