Simplex Solution Method Answer Key
Module A: The Simplex Solution Method
PROBLEM SUMMARY
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. *13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. *28. *29. *30. 31. 32. 33. 34. Simplex short answer Simplex discussion short answer Simplex short answer Simplex short answer Simplex short answer Simplex short answer 4 tableaus 2 tableaus 3 tableaus 3 tableaus 2 tableaus 5 tableaus 5 tableaus 5 tableaus 6 tableaus 4 tableaus 3 tableaus 3 tableaus 3 tableaus Simplex short answer 3 tableaus 4 tableaus graphical analysis 2 tableaus 2 tableaus 6 tableaus 5 tableaus graphical analysis Mixed constraint model transformation Mixed constraint model transformation 5 tableaus 3 tableaus 3 tableaus 4 tableaus 50. 51. 52. 53. 54. *49. *47. *48. 46. 44. 45. 43. 35. 36. 37. 38. 39. 40. 41. *42. 3 tableaus, multiple optimal 4 tableaus 3 tableaus, multiple optimal 2 tableaus, infeasible 2 tableaus, unbounded 4 tableaus, pivot row and column ties, multiple optimal Infeasible problem Dual formation and interpretation, sensitivity analysis Dual formation and interpretation, sensitivity analysis Dual formation and interpretation, sensitivity analysis Dual formation and interpretation, sensitivity analysis Dual formation and interpretation, sensitivity analysis Dual formation and interpretation, sensitivity analysis Dual formation and interpretation, sensitivity analysis Dual formation and interpretation, sensitivity analysis Dual formation and interpretation, sensitivity analysis Sensitivity analysis, cj and qi Sensitivity analysis with duality Sensitivity analysis with duality Sensitivity analysis with duality
253
PROBLEM SOLUTIONS
1. a) x1 = 10, x2 = 40, s3 = 30, z = 420 b) Yes; all cj – zj row values are zero or negative. c) x3 = 0; s2 = 0 d) Maximize Z = 10x1 + 2x2 + 6x3 e) 3Á f) Since there are three decision variables, a three-dimensional graph is required. a) minimization; because zj – cj is being calculated on the bottom row and not cj – zj b) x1 = 20, x3 = 10, s1
PROBLEM SUMMARY
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. *13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. *28. *29. *30. 31. 32. 33. 34. Simplex short answer Simplex discussion short answer Simplex short answer Simplex short answer Simplex short answer Simplex short answer 4 tableaus 2 tableaus 3 tableaus 3 tableaus 2 tableaus 5 tableaus 5 tableaus 5 tableaus 6 tableaus 4 tableaus 3 tableaus 3 tableaus 3 tableaus Simplex short answer 3 tableaus 4 tableaus graphical analysis 2 tableaus 2 tableaus 6 tableaus 5 tableaus graphical analysis Mixed constraint model transformation Mixed constraint model transformation 5 tableaus 3 tableaus 3 tableaus 4 tableaus 50. 51. 52. 53. 54. *49. *47. *48. 46. 44. 45. 43. 35. 36. 37. 38. 39. 40. 41. *42. 3 tableaus, multiple optimal 4 tableaus 3 tableaus, multiple optimal 2 tableaus, infeasible 2 tableaus, unbounded 4 tableaus, pivot row and column ties, multiple optimal Infeasible problem Dual formation and interpretation, sensitivity analysis Dual formation and interpretation, sensitivity analysis Dual formation and interpretation, sensitivity analysis Dual formation and interpretation, sensitivity analysis Dual formation and interpretation, sensitivity analysis Dual formation and interpretation, sensitivity analysis Dual formation and interpretation, sensitivity analysis Dual formation and interpretation, sensitivity analysis Dual formation and interpretation, sensitivity analysis Sensitivity analysis, cj and qi Sensitivity analysis with duality Sensitivity analysis with duality Sensitivity analysis with duality
253
PROBLEM SOLUTIONS
1. a) x1 = 10, x2 = 40, s3 = 30, z = 420 b) Yes; all cj – zj row values are zero or negative. c) x3 = 0; s2 = 0 d) Maximize Z = 10x1 + 2x2 + 6x3 e) 3Á f) Since there are three decision variables, a three-dimensional graph is required. a) minimization; because zj – cj is being calculated on the bottom row and not cj – zj b) x1 = 20, x3 = 10, s1