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# recn8 - A = 1-1 3 5 1 1 2 4 Extracting a column>> A,2...

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ORIE 3300/5300 RECITATION 8 Fall 2010 Wednesday October 27 – Tuesday November 2. Do this exercise with your declared partner (if you have one). Use the Revised Simplex Method to solve the following linear programming problem (in standard inequality form). maximize c T x subject to Ax b x 0 , where A = 1 2 1 1 3 2 3 1 2 , c = 1 7 4 , b = 5 9 8 . Use MATLAB to do the calculations. A quick review of MATLAB is below. Introduce slack variables ﬁrst, and use them as the initial basic variables. Use the largest reduced cost rule to choose the entering variable. At each step, clearly show the basis, the current values of the basic variables, the vector y , the top-row coeﬃcients ¯ c j you compute, the entering index, the vector d , the number t , and the leaving index. Also use MATLAB to compute the ﬁnal tableau. Useful MATLAB commands Entering a vector: >> f = [1 0 2 -1] f = 1 0 2 -1 Transposition: >> c = f’ c = 1 0 2 -1 Entering a matrix: 1

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>> A = [1 -1 3 5 ; 1 1 2 4]

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Unformatted text preview: A = 1-1 3 5 1 1 2 4 Extracting a column: >> A(:,2) ans =-1 1 A list of subscripts: >> B = [2 4] B = 2 4 Extracting the matrix with those corresponding columns: >> E = A(:,B) E =-1 5 1 4 b = [2 ; 7] b = 2 7 Solving the equation E * x = b: >> x = E\b x = 3 1 2 Checking the answer: >> E * x ans = 2 7 >> d = [6 ; 3] d = 6 3 Scalar multiplication: >> 2*d ans = 12 6 Vector addition: >> b+d ans = 8 10 Finding a subset of the indices of a vector: >> c c = 1 2-1 >> indpos = find(c > 0) indpos = 3 1 3 Elementwise division of vectors: >> b./d ans = 0.3333 2.3333 Computing the minimum entry in a vector: minrat = min(b./d) minrat = 0.3333 or [minrat,index] = min(b./d) minrat = 0.3333 index = 1 Keeping a record of your work in the ﬁle my-work : >> diary my-work Turning oﬀ the diary: >> diary off 4...
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recn8 - A = 1-1 3 5 1 1 2 4 Extracting a column>> A,2...

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