1.5.3 More Examples of Optimization Problems.
In this section we look at some more examples of optimization problems that illustrate some of the
mathematical issues that arise in their solution.
Example 1. (a) Find the maximum of z = x2y where x and y mus
1.7 Linear programming - finding a feasible vertex
Now we look at how to modify the simplex method if the starting vertex is not in the feasible region. We illustrate the
technique with the following example.
Example 1. Bill is a fussy eater and only eats
1.6 Linear programming
Linear programming problems are a special class of optimization problems. They are characterized by the following
The quantity to be optimized is a linear function of the independent variables.
The independent va
1.5 Constrained Optimization.
1.5.1 General Principles.
Sometimes we want to find the maximum or minimum of an objective function z = f(x, y) of two
variables x and y, but the two variables x and y are not independent. Rather they must satisfy some
1.8 Linear programming - Duality
In order to illustrate duality let's look at Example 1 of the previous section.
Example 1. Bill eats ham and eggs, but only enough to get the minimum daily requirements (MDR) of
protein and vitamins.
1. Each pound of ham c