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Due to the notable increase in industrial buildings in Ecuador, it is necessary to carry out a technical-economic analysis to know the impact of the cost of materials on them. To do this, a sample of 40 bays was drawn up, establishing the relationship between free span (L), portico height (H) and distance between porticoes (B), in order to determine a metric. For this study, the weight of the structure was established in kg / m². With the results, a mathematical model was applied (Lagrange interpolation), a polynomial was obtained that describes the model of each group of ships and its graphic representation, therefore, an approximation of the weight of structures was determined. The metrics that were found have a direct impact on the cost of the materials of the structures, these were obtained by multiplying them by the cost of the kg of steel. A check was carried out with a sample of 6 ships, in which the weight was found using the design by load and resistance factors and then with the polynomial; obtaining an error: for ships modulated at 5 m an average of 0.03 % with a deviation of 0.03 and for ships modulated at 6 m, an average of 0.07 % with a deviation of 0.03. [ABSTRACT FROM AUTHOR]

This article discusses the use of Lagrange multipliers to solve the optimization model of Markowitz portfolios applied to assets in the stock market of the Stock Exchange of Colombia, in a given time period. Using Lagrange multipliers, the optimal selection method of portfolios, the model solves nonlinear programming (NLP) by a new function resulting from the linear combination between the objective function and the constraints posed by original problem Markowitz . The benefit of this methodology excels is the speed in the outcome of the investment percentages suggested to a percentage change in the expected return. This is crucial when making a buy position and / or sale in the market because of the speed with which the market moves in intraday trading. [ABSTRACT FROM AUTHOR]