x 1 120 x 1 x 2 100 200 x 1 20x 2 x 10 000x 1 x 2 x3 LP0 1stiteration

X 1 120 x 1 x 2 100 200 x 1 20x 2 x 10 000x 1 x 2 x3

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x 1 1 20 x 1 + x 2 100 200 x 1 + 20 x 2 + x 10 , 000 x 1 , x 2 , x 3 0 . LP0: 1 st iteration: >> dictionary dict = ' ' ' ' 'w4' 'w5' 'w6' 'zeta' [9.1000e+03] [-100.0000] [ 10.0000] [ -1.0000] 'x1' [ 1.0000] [ -1.0000] [-2.7756e-17] [ 1.7347e-18] 'x2' [ 80.0000] [ 20.0000] [ -1.0000] [-2.7756e-17] 'x3' [8.2000e+03] [-200.0000] [ 20.0000] [ -1.0000] 2 nd iteration: Leaving – 2; Entering - 5 >> dictionary dict = ' ' ' ' 'w4' 'x2' 'w6' 'zeta' [9900] [100] [-10] [-1] 'x1' [ 1] [ -1] [ 0] [ 0] 'w5' [ 80] [ 20] [ -1] [ 0] 'x3' [9800] [200] [-20] [-1] 3 rd iteration: Leaving – 4; Entering - 1 >> dictionary
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dict = ' ' ' ' 'x1' 'x2' 'w6' 'zeta' [10000] [-100] [-10] [-1] 'w4' [ 1] [ -1] [ 0] [ 0] 'w5' [ 100] [ -20] [ -1] [ 0] 'x3' [10000] [-200] [-20] [-1] Optimal solution: Zeta*= 10000; x 1 * = 0; x 2 * = 0; x 3 * = 10000; w 4 * = 0; w 5 * = 0; w 6 * = 0; (b) Max x ζ = −x 1 − x 2 s . t . 2 x 1 − x 2 4 2 x 1 + 4 x 2 ≤ − 8 −x 1 + 3 x 2 7 x 1 , x 2 0 . Max x, w ζ = −x 1 − x 2 s . t . 2 x 1 − x 2 + ω 3 = 4 2 x 1 + 4 x 2 + ω 4 = − 8 −x 1 + 3 x 2 + ω 5 = 7 x 1 , x 2 , ω 3 , ω 4 , ω 5 0 Min x,w,t t 6 + t 7 s . t . 2 x 1 − x 2 + ω 3 = 4 2 x 1 + 4 x 2 + ω 4 – t 6 = − 8 −x 1 + 3 x 2 + ω 5 –t 7 = 7 x 1 , x 2 , ω 3 , ω 4 , ω 5 , t 6 , t 7 0 LP1: Iteratio n B N Enterin g Leavin g 1 st 1,2, 3 4,5, 6 N/A N/A 2 nd 1,5, 3 4,2, 6 5 2 3 rd 4,5, 3 1,2, 6 4 1
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Table 1 Dictionary for LP1 1 st Iteration >> dictionaryLP1 Error using dictionaryLP1 (line 15) Not enough input arguments. 2 nd Iteration >> dictionaryLP1 Error using dictionaryLP1 (line 26) (B,N) is not a feasible basic partition 3 rd Iteration >> dictionaryLP1 Error using dictionaryLP1 (line 20) N should have 4 elements 4 th Iteration >> dictionaryLP1 Error using dictionaryLP1 (line 26) (B,N) is not a feasible basic partition 5 th Iteration >> dictionaryLP1 Error using dictionaryLP1 (line 26) (B,N) is not a feasible basic partition 6 th Iteration >> dictionaryLP1 Iteratio n B N Entering Leavin g fbs 1 st 1,2, 3 4,5,6,7 4 3 No 2 nd 1,2, 4 3,5,6,7 5 4 No 3 rd 1,2, 5 3,4,6,7 6 5 No 4 th 1,2, 6 3,4,5,7 7 6 No 5 th 1,2, 7 3,4,5,6 4 7 Yes 6 th 1,3, 4 2,7,5,6 N/A N/A OPTIMAL
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Error using dictionaryLP1 (line 26) (B,N) is not a feasible basic partition 7 th Iteration >> dictionaryLP1 Error using dictionaryLP1 (line 26) (B,N) is not a feasible basic partition 8 th Iteration >> dictionaryLP1
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