# hw2 - x cannot be an optimal solution to this LP 3 Consider...

This preview shows page 1. Sign up to view the full content.

AMS 540 / MBA 540 (Fall, 2010) Estie Arkin Homework Set # 2 Due in class on Thursday, September 23, 2010. 1). (a) Show that the set of all feasible solutions to the following linear program forms a convex set: min { cx | Ax = b, x 0 } (b) Prove that the set of optimal solutions to the linear program (of part (a)) forms a convex set. 2). Consider the linear program: Minimize cx subject to Ax b, x 0, where c is a non zero vector. Suppose that a point x 0 is such that Ax 0 < b and x 0 > 0. Show (prove) that
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x cannot be an optimal solution to this LP. 3). Consider an LP: ( p 1 and p 2 are given constants.) max z =-p 1 x 1 + p 2 x 2 x 1-x 2 = 0 ≤ x 1 , x 2 ≤ 1 (a). What are the extreme points and extreme directions of this LP? (b). Write the equivalent LP in terms of the extreme points and extreme directions. (c). Now suppose that p 1 > p 2 . What is the optimal solution to the LP? (Make sure to state z as well as x 1 , x 2 .)...
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