VI Sem ECE Assignment of Optimization Techniques

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Q.8. Solve graphically the following LP problemMaximize 4 x 1 + 3 x 2Subject to2x 1 +3 x 2 ≤ 64 x 1 + 6 x 2 ≥ 24x 1 , x 2 ≥ 0Q.9. Solve graphically the following LP problemMaximize 3 x 1 + 2 x 2Subject to2x 1 - 3 x 2 ≥ 03 x 1 + 4 x 2 ≤ -12x 1 , x 2 ≥ 0(b) Multiple Solution ProblemQ.10. Solve graphically the following LP problemMaximize x 1 + x 2Subject to-2x 1 + x 2 ≤ 1x 1 ≤ 2x 1 + x 2 ≤ 3x 1 , x 2 ≥ 0Q.11. Differentiate between surplus , slack variables and artificial variables?Q.12. What is degeneracy problem in relation to linear programming problem?
Simplex MethodQ.13. Solve the L.P. ProblemMaximize x 1 + 2 x 2 + x 3Subject to2x 1 + x 2 - x 3 ≤ 22 x 1 - x 2 + 5 x 3 ≤ 64x 1 + x 2 + x 3 ≤ 6x i ≥ 0, i=1,2,3Q.14. Solve the L.P. ProblemMaximize Z = 2 x 1 + 6 x 2Subject to-x 1 + x 2 ≤ 12 x 1 + x 2 ≤ 2x 1 , x 2 ≥ 0Q.15. Solve the L.P. ProblemMaximize Z = 6 x 1 + 8 x 2Subject to2x 1 + 3x 2 ≤ 164 x 1 + 2x 2 ≤ 16x 1 , x 2 ≥ 0Q.16. Solve the L.P. ProblemMinimize x 1 - 3 x 2 + 2x 3
Page 1 and 2: VI Sem ECEAssignment of Optimizatio
Page 3: of X2 must be used. Find how much o
Page 7 and 8: 4 x 1 + 3 x 2 ≥ 6x 1 + 2 x 2 ≤
Page 9 and 10: DualityQ.26. Write the dual of the
Page 11: x 1 + 2x 2 + x 3 + x 4 = 10x i ≥

VI Sem ECE Assignment of Optimization Techniques

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