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Unformatted text preview: insights into integer programming that have led to other, more efficient, algorithms. Again, we shall discuss the method by considering the sample problem of the previous sections: z# = max 5x1 + 8x2, subject to: x1 + x2 + s1 = 6, 5x1 + 9x2 + s2 = 45, x1, x2, s1, s2 # 0. (11) s1 and s2 are, respectively, slack variables for the first and second constraints. Solving the problem by the simplex method produces the following optimal tableau: (z) 5 4 s1 3 4 s2 = 411 4 , x1 +9 4 s1 1 4 s2 = 9 4 , x2 5 4 s1 +1 4 s2 = 15 4 , x1, x2, s1, s2, s3 # 0. Let us rewrite these equations in an equivalent but somewhat altered form: (z) 2s1 s2 +42 = 3 4 3 4 s1 1 4 s2, x1 +2s1 s2  2 = 1 4 1 4 s1 3 4 s2, x2 2s1  3 = 3 4 3 4 s1 1 4 s2, x1, x2, s1, s2 # 0....
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 Spring '11
 ProfBhattacharya

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