Analysis of Technological Relationships Using Production Function in Manufacturing Industries

In this paper, we explain how the technological relationship of the production inputs and outputs. In an effort to reach the target production, which depends on different factors such as land, labor and capital, manufacturing industries seek to determine the optimal amount of labor. It aims to ensure the efficient use of labor to face the competitive global market. By using an applied mathematical production function we could inform industrial policies about the production inputs and outputs. In the current era of globalization, mathematics is very actively applied in various aspects of society, such as a variety of functions in the analogy of mathematics into related activities between one variable (person) and with another variable (or any other group of people). Such functions include exponential functions, trigonometric functions, quadratic functions, logarithmic functions and others. The Cobb-Douglas production function is widely used to represent the technological relationship between the amounts of two or more inputs, particularly physical capital and labor, and the amount of output that can be produced by those inputs. This function indicates how the elasticity of production, in which this elasticity describes how much influence (in percent) to the output obtained. The Cobb-Douglas function also shows a return to scale (RTS) that explains how the production conditions of an industry. The RTS also explains how the combination of inputs used to obtain optimal output. The result of the research, we get the production elasticity of the capital is greater than the labor. And we get $\mathbf{RTS} > 1$ which shows that the condition of industry is increasing return to scale.