Page 869 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

If the objective function of a linear programming problem has the same value at two adjacent extreme points, show that it has
10. the same value at all points on the straight line segment connecting the two extreme points.

Hint If and are any two points in the plane, a point lies on the straight line segment connecting
them if

and

where t is a number in the interval [0, 1].

Show that the objective function in Example 10 attains a maximum value in the feasible set.
11.

Hint Examine the level curves of the objective function.

Section 11.3

Technology Exercises

The following exercises are designed to be solved using a technology utility. Typically, this will be MATLAB, Mathematica, Maple,
Derive, or Mathcad, but it may also be some other type of linear algebra software or a scientific calculator with some linear algebra
capabilities. For each exercise you will need to read the relevant documentation for the particular utility you are using. The goal of
these exercises is to provide you with a basic proficiency with your technology utility. Once you have mastered the techniques in
these exercises, you will be able to use your technology utility to solve many of the problems in the regular exercise sets.

Consider the feasible region consisting of , along with the set of inequalities
T1.

for , 1, 2, …, . Maximize the objective function , and (k)

assuming that (a) , (b) , (c) , (d) , (e) , (f) , (g) , (h) , (i) , (j)
. (l) Next, maximize this objective function using the nonlinear feasible region, , , and

(m) Let the results of parts (a) through (k) begin a sequence of values for . Do these values approach the value determined
in part (l)? Explain.

Repeat Exercise T1 using the objective function .
T2.

Copyright © 2005 John Wiley & Sons, Inc. All rights reserved.