ISE 330: Introduction to Operations Research

Transcription

1 ISE 0: Introduction to Operations Research Fall 00: Thursday, December, - Instructor: Elaine Chew Final Exam 8 Pages Total hours Exams?! We re still getting exams? -- Seamus Finnigan Yes, you are. Please take the exam. Enjoy! Question Part Total Score (a) 0 (b) 0 (c) (a) 0 (b) (c) (d) 0 (e) 0 (f) 0 0 Name: In case you re wondering who is Seamus Finnigan, he is a Gryffindor in Harry Potter s year. "I'm a half and half," said Seamus. "Me dad's a Muggle. Mom didn't tell him she was a witch 'till after they were married. Bit of a nasty shock for him." He is "sandyhaired" in the book and posesses much Irish pride. Seamus enjoys Quidditch and flying. The way he tells it, he "spent most of his childhood zooming around the countryside on a broomstick." ~ From Insignificant Harry Potter Characters Who Are Hot (

2 Question : The following questions are based on the following LP. Min x + x s.t. x + x x x x x x 0, x 0 (a) Please solve the linear program graphically, showing the objective function, all constraints, the feasible region and marking all basic solutions (distinguishing the ones that are feasible). [ 0 points ] E.C.

3 (b) Without solving the dual problem, what can you say about the feasible region and all corresponding solutions in the dual? [ 0 points ] Primal Dual Feasible region Corner pt solution : Corner pt solution : Corner pt solution : Etc. E.C.

4 (c) Suppose the objective function was Z = ( + q)x + x. Determine the values of q for which the optimal solution is at each of the corner point feasible solutions. [ points ] E.C.

5 . According to the online Wikipedia, When you hold a remembrall, it turns red if you've forgotten something. Unfortunately, it does not tell you what you have forgotten. Remembralls are a hot Christmas item this season. The parameter table below shows the supply and and of remembralls this Christmas, and the cost (by Owl Post) to ship a remembrall from each supplier to each wizarding acay. Fluorish and Blotts Gambol and Japes Dervish and Banges Zonko s Joke Shop Hogwarts School of Witchcraft and Wizardry Beauxbatons Acay of Magic Durmstrang Institute (a) Use a graph to represent this transportation network. [ 0 points ] E.C.

6 (b) Use the Northwest Corner Rule to construct an initial Basic Feasible Solution. You may use the boxes below to document your solution. [ points ] supp E.C. 6

7 (c) Use the Vogel s Approximation Method to construct another initial Basic Feasible Solution. [ points ] Iteration : supp u i v j E.C. 7

8 Iteration : supp u i v j E.C. 8

9 Iteration : supp u i v j E.C. 9

10 Iteration : supp u i v j E.C. 0

11 Iteration : supp u i v j E.C.

12 Iteration 6: supp u i v j E.C.

13 Iteration 7: supp u i v j E.C.

14 (d) Using either your solution from part (b) or part (c), perform one iteration of the transportations simplex method. Show both the table before and after the iteration, and be sure to highlight the cycle created. [ 0 points ] Before: supp u i v j E.C.

15 After: supp E.C.

16 (e) Using either your solution from part (b) or part (c), create a graph to represent this basic feasible solution for the corresponding minimum cost flow problem. [ 0 points ] E.C. 6

17 (f) Proceed to perform one iteration of thenetwork simplex method. Show both the graph before and after the iteration. Be sure to highlight the cycle created. [ 0 points ] Graph before iteration: Iteration : Nonbasic Arc Cycle Created DZ when q = E.C. 7

18 Graph after iteration: Question : Extra credit. (a) Hogwarts is located in (country) [ points ] (b) A squib is [ points ] E.C. 8