Lecture 1 - Topic 1 Introduction to Linear Programming Example(Matrix Transpose Row Column 2 3 4 A= 5 8 9 x1 x2 B= xn Column Vector 2 5 A = 3 8 4 9

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Topic 1 Introduction to Linear Programming
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Example (Matrix Transpose) 234 589  =   A 25 ' 38 49 = A 1 2 n x x x = B ( ) 12 ' n xx x = B Column Row Column Vector Row Vector
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Example (Column Vectors) 1 2 n x x x   =  x ( ) 12 ' n xx x = x Column Vector Row Vector vector. a by denoted always is in vector l dimensiona an course, For this : Note column R n n x
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1 2 n x x x   =  x ( ) 12 ' n xx x = x Column Vector Row Vector ( ) 1 2 ' n n x x x x = Note : ( ) Thus, we may write ' n x = x
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1 2 n x x x   =  x 1 2 n y y y = y ( ) 12 ' n yy y = y ( ) ' n xx x = x ( ) n n n n y x y x y x y y y x x x + + + = = 2 2 1 1 2 1 2 1 ' y x ( ) n n n n y x y x y x x x x y y y + + + = = 2 2 1 1 2 1 2 1 ' x y
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1 2 n x x x   =  x ( ) 1 2 12 11 2 2 ' n n nn x x cc c x cx cx cx = = ++ + 1 2 n c c c = c ( ) ' n xx x = c Cost function : = = n i i i x c 1
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1 2 n x x x   =  x ( ) 1 2 12 11 2 2 ' n n nn x x cc c x cx cx cx = = ++ + 1 2 n c c c = c 124 2 xx x ++≥ Vector form ( ) = + + 4 3 2 1 4 2 1 1 0 1 1 x x x x x x x ( ) 2 1 0 1 1 4 3 2 1 x x x x
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124 2 xx x ++≥ ( ) 1 2 3 11 0 1 2 n x x x x    Example 1.3 23 35 −= ( ) 1 2 3 0 3 10 5 n x x x x ( ) 1 2 3 0 0 3 n x x x x 3 4 3 + x x
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( ) 3 1 1 0 0 4 3 2 1 x x x x ( ) 4 3 2 1 0 4 1 2 x x x x ( ) 2 1 0 1 1 4 3 2 1 x x x x ( ) 5 0 1 3 0 4 3 2 1 =
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This note was uploaded on 12/02/2011 for the course MATH 3252 taught by Professor Tanbanpin during the Spring '10 term at National University of Singapore.

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Lecture 1 - Topic 1 Introduction to Linear Programming Example(Matrix Transpose Row Column 2 3 4 A= 5 8 9 x1 x2 B= xn Column Vector 2 5 A = 3 8 4 9

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