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What is the significance of duality theory of linear programming Describe the general rules for writing the dual of a linear programming problem?
the significance of duality theory of linear programming
What is a self dual polyhedron?
For every polyhedron, there is a dual which is a polyhedron that has:a face where the first had a vertex,a vertex where the first had a face,the same number of edges.A self-dual polyhedron is a polyhedron whose dual is the same shape.All pyramids, for example, are self-dual.
What is the difference between the primal and dual?
The difference between primal and dual are that primal means an essential, or fundamental of an aspect where as dual means consisting of two parts or elements. Primal is one, dual is two.
What is the principle of duality in boolean algebra?
There is a dual for every Boolean operation. For example the dual of (a AND b) is not(not A or not B). The first says TRUE if a and b are both TRUE. The second says that FALSE if a is FALSE or b is FALSE. Both statements are equivalent. This equivalency is also referred to by DeMorgan's Theorem.
What is a dual?
A dual is almost like the opposite of a given polytope. For example, a regular octahedron is the dual of a cube.Look at the similarities between duals with the example of a cube and regular octahedron:Cube:Vertices: 8Edges: 12Faces: 6Edges per vertex: 3Type of face: square (4-sided)Regular Octahedron:Vertices: 6Edges: 12Faces: 8Edges per vertex: 4Type of face: triangle (3-sided)Both of these shapes can be put together to form a compound and can be rectified to form the same new shape: a cuboctahedron.Also, duals can fit perfectly inside another where each edge touches the face of the other.In this same way a regular dodecahedron is the dual of a regular icosahedron. Some polyhedra like the regular tetrahedron is the dual of itself. All polyhedra have duals. Polygons, polychora, and other polytopes can also have duals in a similar fashion.
