Homework 8

Homework 8 - (b) Is the vertex optimal? Explain why or why...

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

View Full Document Right Arrow Icon
Math 171A: Mathematical Programming Instructor: Philip E. Gill Winter Quarter 2009 Homework Assignment #8 Due Friday March 6, 2009 The second midterm exam will be held in class on Wednesday, March 4. Starred exercises require the use of Matlab . Exercise 8.1. * Consider the following linear program with mixed constraints minimize x R n c T x subject to Ax = b Dx f. (8.1) (a) Consider the Portfolio Problem described on pages 32–35 of the Class Notes. Formulate the Portfolio Problem in the form ( 8.1 ). (b) Starting at the vertex x 0 = (0, 500, - 10) T , execute the steps of a “mixed-constraint” version of the simplex method that will treat problems with mixed constraints. (Do not write the equality constraint as two inequalities!) Exercise 8.2. Consider the standard-form problem of minimizing c T x subject to Ax = b , x 0, with A = ± 1 1 1 1 1 - 1 - 3 2 ² , b = ± 1 - 2 ² and c = - 1 0 - 2 0 . (a) Use any method of your choice to find a vertex for this constraint set.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (b) Is the vertex optimal? Explain why or why not. Exercise 8.3. * Consider the linear program minimize x 1 ,x 2 ,x 3 ,x 4-x 2-x 3-2 x 4 subject to x 2 + 2 x 3 1 x 1 + x 2 + x 3 + x 4 1 x 1-x 2-5 x 3 + 3 x 4 1 x 1 x 2 x 3 x 4 . (a) Convert this problem into standard-form min c T x subject to Ax = b , x 0. (b) Compute one iteration of the standard-form simplex method for this problem, starting at the basic solution x B = ( 1 2 , 1 2 , 2) T dened by columns 3, 4 and 7 of A . Show your work. Be sure to write down the objective function, basic set, nonbasic set, -vector and reduced costs at both the beginning and end of the iteration. Check that the new iterate is feasible, with improved objective value....
View Full Document

This note was uploaded on 10/23/2010 for the course MATH 171a taught by Professor Staff during the Winter '08 term at UCSD.

Ask a homework question - tutors are online