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Section 3.3 Solving NonCanonical Problems with Sage
In
Section 2.4 , we showed how to use Sage to solve canonical linear optimization problems with the Simplex Algorithm. In this section, we use Sage to solve noncanonical problems.
Activity 3.3.1 .
Say we want to solve the noncanonical linear optimization problem:
\begin{align*}
\textbf{Minimize: } f(\mathbf{x}) & = 3x+y+2z\\
\textbf{subject to: } x+2y+3z& \geq 24\\
2x+4y+3z& = 36\\
y, z& \geq 0.
\end{align*}
(a) Record this noncanonical problem using Sage:
(b) Find the optimal solution:
Note that we use the command
InteractiveLPProblem rather than
InteractiveLPProblemStandardForm for general (potentially noncanonical) linear optimization problems. Sage does not have a command for the Simplex Algorithm for
InteractiveLPProblem.
Activity 3.3.2 .
Solve:
\begin{align*}
\textbf{Minimize: } f(\mathbf{x}) & = -5x+y-2z\\
\textbf{subject to: } 2x+z& = 0\\
x-y& \geq 1\\
3x-y+z& \leq 3.
\end{align*}
