This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: IEOR 162 Linear Programming Spring 2007 Midterm Solutions 1. a. False. Consider the LP max { x 1 + x 2 : x 1 + x 2 2 , x 1 , x 2 } , for which one optimal solution is x 1 = x 2 = 1, which is clearly not a basic feasible solution (since only 1 of the 3 constraints is active at that point). b. False. The problem could be unbounded, in which case x is not an optimal solution. c. False. The correct statement is x is a basic feasible solution if and only if x is an extreme point. d. False. Consider the LP max { x 1 + x 2 : x 1 + x 2 2 , x 1 , x 2 } , for which the following two points are feasible: x 1 = (2 , 0) and x 2 = (0 , 2). Now let = 2, then x 1 + (1 ) x 2 = (4 , 0) (0 , 2) = (4 , 2), which is clearly not a feasible solution. e. False. At each iteration of the simplex method, it is possible for all of the basic variables values to change as well as one nonbasic variable. 2. a. Standard Form: max 5 x 1 s.t. 2 x 1 x + 3 + x 3 + s 1 = 0 x 2 + 3 x + 3 3 x 3 e 2 = 0 x 1 + x 2 + s 3 = 0 6 x 1 7 x 2 = 0 x 1 , x 2 , x + 3 , x 3 , s 1 , e 2 , s 3...
View
Full
Document
This homework help was uploaded on 04/02/2008 for the course IEOR 162 taught by Professor Zhang during the Spring '07 term at University of California, Berkeley.
 Spring '07
 Zhang

Click to edit the document details