# Using the gomory cutting plane algorithm solve the

• Notes
• 5

This preview shows pages 2–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Using the Gomory cutting plane algorithm, solve the original IP problem. Do not add more than two cutting planes. (14 marks) AMA405 2 Continued AMA405 3 (i) With reference to the following linear programming problem: maximise z = x 1 + 2 x 2 subject to x 1 + x 2 10 2 x 1 + 3 x 2 10 3 x 1 + 2 x 2 = 10 x 1 ; x 2 give reasons for the need for arti cial variables and indicate how the Simplex method can be modi ed to take account of them. (4 marks) (ii) Use the Two-Phase Simplex method to solve the problem. (21 marks) AMA405 3 Turn Over AMA405 4 (i) Using the usual notation, the tableau for the problem maximise z = c T 1 x 1 + c T 2 x 2 subject to A x 1 + I x 2 = b x 1 ; x 2 ; at a stage in the Simplex algorithm when the basis matrix is B , is repre- sented by " 1 c T B B 1 A c T 1 c T B B 1 c T 2 B 1 A B 1 # z x 1 x 2 = " c T B B 1 b B 1 b # where x 2 is the starting basis. (a) Write down the conditions necessary for this tableau to be optimal. (3 marks) (b) Write down an expression for the optimal dual variables in terms of the notation above and verify that the dual constraints are satis ed. (7 marks) (ii) In the context of deriving the dual of a maximisation linear programming problem, describe the transformations necessary to convert the following into the Standard Form: (a) 4 x 1 + 3 x 2 = 10 (b) x 3 unrestricted (c) minimise z = 10 x 1 + 3 x 2 (d) 2 x 1 x...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern