Page 270 -

250 CHAPTER 5 LINEAR PROGRAMMING: THE SIMPLEX METHOD

a. Complete the initial tableau.
b. Write the problem in tableau form.
c. What is the initial basis? Does this basis correspond to the origin? Explain.
d. What is the value of the objective function at this initial solution?
e. For the next iteration, which variable should enter the basis, and which variable should
leave the basis?
f. How many units of the entering variable will be in the next solution? Before making this
first iteration, what do you think will be the value of the objective function after the first
iteration?
g. Find the optimal solution using the Simplex method.
7 Solve the following linear programme using the graphical approach:
Max 4x 1 þ 5x 2
s:t:
2x 1 þ 2x 2 20
3x 1 þ 7x 2 42
x 1 ; x 2 0
Put the linear programme in tableau form, and solve using the Simplex method. Show the
sequence of extreme points generated by the Simplex method on your graph.
8 Recall the problem for GulfGolf introduced in Section 2.1. The mathematical model for this
problem is restated as follows:

Max 10x 1 þ 9x 2
s:t:
0:7x 1 þ 1x 2 630 Cutting and sewing
0:5x 1 þ 0:8333x 2 600 Sewing
1x 1 þ 0:6667x 2 708 Finishing
0:1x 1 þ 0:25x 2 135 Inspection and packaging
x 1 ; x 2 0
where
x 1 ¼ number of standard bags produced

x 2 ¼ number of deluxe bags produced
a. Use the Simplex method to determine how many bags of each model GulfGolf should
manufacture.
b. What is the profit GulfGolf can earn with these production quantities?
c. How many hours of production time will be scheduled for each operation?
d. What is the slack time in each operation?
9 Solve the RMC problem (Chapter 2, Problem 12) using the Simplex method. At each
iteration, locate the basic feasible solution found by the Simplex method on the graph of
the feasible region. The problem formulation is shown here:
Max 40x 1 þ 30x 2
s:t:
0:4x 1 þ 0:5x 2 20 Material 1
0:2x 2 5 Material 2
0:6x 1 þ 0:3x 2 21 Material 3
x 1 ; x 2 0

Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has
deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.