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Math 482 (Lecture 2): Standard and canonical forms
Today: Continue to discuss 2.1 of the textbook
Last class we discussed the diet problem as an example of a linear programming problem.
We now wish to work to systematize a method to solve such problems.
* In order to do so, we need to decide on some conventions (if only to be able to talk to a
computer).
* For brevity, the course often makes heavy use of matrix notation. This can be confusing
(and will no doubt confuse me at some point), but it is the most efficient way to write
down ideas in many cases.
* Consider the following problem:
minimize c'x
Ax≥ r
x≥ 0
This is the
canonical form
of the LP problem. Here:
 x is a length n COLUMN vector
 c is a length n COLUMN vector, c' is the transpose ROW vector
 A is an mxn matrix
 r is a length m COLUMN vector
Note:
Some textbooks say that the canonical form uses Ax≤ r, or replace maximize by
minimize (can you see why neither of these makes much difference?).
In class exercise:
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 Spring '08
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 Linear Programming

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