chapter7-1 - 1).1 Chapter 7 Chapter 7 Duality Theory...

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Unformatted text preview: 1).1 Chapter 7 Chapter 7 Duality Theory Duality Theory The theory of duality is a very elegant and important concept within the field of operations research. This theory was first developed in relation to linear programming, but it has many applications, and perhaps even a more natural and intuitive interpretation, in several related areas such as nonlinear programming, networks and game theory. 1).2 ✿ The notion of duality within linear The notion of duality within linear programming asserts that every linear programming asserts that every linear program has associated with it a related program has associated with it a related linear program called its linear program called its dual . The original . The original problem in relation to its dual is termed the problem in relation to its dual is termed the primal . . ✿ it is the it is the relationship between the primal between the primal and its dual, both on a mathematical and and its dual, both on a mathematical and economic level, that is truly the essence of economic level, that is truly the essence of duality theory. duality theory. 1).3 7.1 Examples 7.1 Examples ✿ There is a small company in Melbourne which has There is a small company in Melbourne which has recently become engaged in the production of office recently become engaged in the production of office furniture. The company manufactures tables, desks furniture. The company manufactures tables, desks and chairs. The production of a table requires 8 kgs and chairs. The production of a table requires 8 kgs of wood and 5 kgs of metal and is sold for $80; a desk of wood and 5 kgs of metal and is sold for $80; a desk uses 6 kgs of wood and 4 kgs of metal and is sold for uses 6 kgs of wood and 4 kgs of metal and is sold for $60; and a chair requires 4 kgs of both metal and $60; and a chair requires 4 kgs of both metal and wood and is sold for $50. We would like to determine wood and is sold for $50. We would like to determine the revenue maximizing strategy...
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This note was uploaded on 07/08/2011 for the course IE 131 taught by Professor Groover during the Spring '08 term at Lehigh University .

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chapter7-1 - 1).1 Chapter 7 Chapter 7 Duality Theory...

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