Name:
SA305 – Linear Programming
Asst. Prof. Nelson Uhan
Spring 2016
Quiz 8
Instructions. You have 15 minutes to complete this quiz. You may use your notes, homework, textbook, and calculator.
Suppose you are in the midst of performing the simplex method on the following canonical form LP:
maximize
3x1 + 2x2 − x3 + 4x4
subject to
x1 − 3x2 + x3
=7
x2 + 2x3 + 4x4 = 8
x1 ,
x2 ,
x3 ,
x4 ≥ 0
The current BFS is x t = (7, 0, 0, 2) with basis B t = {x1 , x4 }. You have already done the following simplex method
computations:
1
dx3 = ( − 1, 0, 1, − )
2
c̄ x3 = −6
a. (10 points) Compute all the remaining simplex directions and associated reduced costs at x t .
(over)
b. (10 points)
i. Without doing any further computations:
● Can you conclude that x t is optimal?
● Can you conclude the LP is unbounded?
Why or why not?
ii. If x t is not optimal and the LP is not unbounded based on the current iteration, compute x t+1 and B t+1 .