Our 12th grade Math Honors students are able to construct a mathematical model using systems of equations, systems of inequalities and matrices to solve these application problems algebraically. Afterwards they apply technology, in particular, Microsoft Excel to create formulas and functions to confirm their solutions.
Many applications in business and economics involve a process called optimization, in which you are asked to find the minimum or maximum value of a quantity. In a free market, the demands for many products are related to the prices of the products. As the prices decrease, the demands by consumers increase and the amounts that producers are able or willing to supply decrease. These two related concepts economists call consumer surplus and producer surplus.
Network analysis, Kirchhoff’s point and loop rules plays an important role in electrical engineering. In recent years, the concepts and tools of network analysis have been found to be useful in many other fields, such as information theory and the study of transportation systems. The following analysis of traffic flow through a road network during the peak period illustrates how systems of linear equations with many solutions can arise in practice.
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