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 non-canonical 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 non-canonical problem using Sage:
(b)
Find the optimal solution:
Note that we use the command InteractiveLPProblem rather than InteractiveLPProblemStandardForm for general (potentially non-canonical) 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*}
