quiz2solutions

# quiz2solutions - the entering and departing variables False...

This preview shows pages 1–2. Sign up to view the full content.

640:354:01, 02/12/07 Quiz #2, with solutions 1. Consider the following LP in standard form: Maximize 2 x 1 + 3 x 2 + x 3 , subject to x 1 + 10 x 2 + x 3 4 x 2 + x 3 2 x 1 + 5 x 2 + x 3 3 x 1 ,x 2 ,x 3 0 Write the corresponding canonical form. Write the initial simplex tableau, and the cor- responding dictionary. Solution: The canonical form is obtained by introducing slack variables: Maximize 2 x 1 + 3 x 2 + x 3 , subject to x 1 +10 x 2 + x 3 + x 4 = 4 x 2 + x 3 + x 5 = 2 x 1 +5 x 2 + x 3 + x 6 = 3 x 1 , x 2 , x 3 , x 4 , x 5 , x 6 0 The simplex tableau is: x 1 x 2 x 3 x 4 x 5 x 6 x 4 1 10 1 1 0 0 4 x 5 0 1 1 0 1 0 2 x 6 1 5 1 0 0 1 3 z -2 -3 -1 0 0 0 0 The corresponding dictionary is: x 4 = 4 - x 1 - 10 x 2 - x 3 x 5 = 2 - x 2 - x 3 - x 5 x 6 = 3 - x 1 - 5 x 2 - x 3 z = 2 x 1 + 3 x 2 + x 3

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

View Full Document
2. Suppose we have a linear program in canonical form. True or false? (If false, justify!) (a) Given an initial basic feasible solution, the simplex method will lead to an optimal solution in ﬁnitely many steps, provided that such a solution exists, no matter how we choose
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: the entering and departing variables. False. Unless we use Bland’s rule, cycling may occur, thus resulting in non-termination of the method. (b) The value of z strictly increases from one tableau to the next, whenever the simplex method is followed. False. The value of z remains the same if the value of the departing variable is zero (that is, if degeneracy occurs). (c) Every row of every tableau, including the objective row, corresponds to an equation which is satisﬁed by all feasible solutions. True. 2...
View Full Document

## This note was uploaded on 09/12/2008 for the course MATH 354 taught by Professor Vogelius during the Spring '08 term at Rutgers.

### Page1 / 2

quiz2solutions - the entering and departing variables False...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online