Analytical Methods

• Published in: Introduction to Optimization for Environmental and Chemical Engineers pp. 83 - 94
• Main Authors: Louis, Theodore, Kelly, Behan
• Format: Book Chapter
• Language: English
• Published: CRC Press 2018
• Edition: 1
• Subjects: Objective Function; Saddle Point; Linear Simultaneous Equations; Sulfuric Acid Process; Part Iii; Optimize Pipe Diameter; Mathematical Optimization Techniques; Air Pollution Management; Minimum Emission; Follow; Health Risk Assessment; General Analytical Formulation; Air Pollution Control Device; Perry’s Chemical Engineers; Intermediate Pressures; Income Optimum; Liquid Feed Mixture; Independent Variable; Model Predictive Control; Steepest Ascent; Excellent Starting Point; Breakeven Figure; Environmental Engineering Calculations; Profit Equation; Hold
• ISBN: 9781138489127; 1138489123
• DOI: 10.1201/9781351037389-7

The subject of analytical methods serves as an excellent starting point before preceding to the last subject in this first Part — linear programming. This chapter provides the various sections: Breakeven Consideration, One Independent Variable, General Analytical Formulation of the Optimum, two Independent Variables and three Independent Variable. In solving many environmental and chemical engineering optimization problems, one often selects optimum conditions from the standpoint of economics. Here the thickness of the cover serves as the independent variable, and if the installed cost of the insulation and the LNG transportation leakage losses could both be determined as functions of the independent variable, a condition would exist for which the total cost is a minimum. The term y is the dependent variable that will later be referred to as the objective function and x is the independent variable.