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 4x 2x 32 x 4 subject to x 2 + 2 x 3 ≤ 1 x 1 + x 2 + x 3 + x 4 ≤ 1 x 1x 25 x 3 + 3 x 4 ≤ 1 x 1 ≥ x 2 ≥ x 3 ≥ x 4 ≥ . (a) Convert this problem into standardform min c T x subject to Ax = b , x ≥ 0. (b) Compute one iteration of the standardform simplex method for this problem, starting at the basic solution x B = ( 1 2 , 1 2 , 2) T deﬁned by columns 3, 4 and 7 of A . Show your work. Be sure to write down the objective function, basic set, nonbasic set, πvector 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
 Winter '08
 staff
 Math, matlab, Optimization, linear program, Philip E. Gill, mixed constraints, min cTx subject

Click to edit the document details