Due to global economic crisis optimization and social welfare become an essential part of the economy and business. Every firm wants output maximization, cost minimization, utility maximization and social welfare. In this book an attempt has been made to maximize an output subject to a budget constraint to maximize utility function subject to multiple constraint and minimization of cost in three variables subject to output function as a constraint, studying the behavior of the firm. It deals with formulating mathematical model for the problem, considering Cobb-Douglas production function in three variables (factors: capital, labor, and other inputs). Considering an explicit form of production function, necessary conditions are applied to the optimization problem, and have been tried to find stationary points as well as optimal value of the production function. In this book Arrow's impossibility theorem, its combinatorial and geometrical interpretation is given more clearly. Social welfare works of Amartya K. Sen are described with easier mathematical calculations.