Introduction This is a followup to a prior post on the same topic, where I used R’s base plotting system to visualize a linear programming provelm. I’m again looking at section 1.4 of Introduction to Linear Optimization. This time, we’ll consider Example 1.8 on page 23 (Bertsimas and Tsitsiklis 1997, 23). The optimization problem in this example is:
\[\begin{align*} -x_1+x_2 &\leq 1 \\ x_1 &\geq 0 \\ x_2 &\geq 0 \end{align*}\]
Some preliminary notes This time, instead of using the base R package, we’re going to plot the problem using the ggplot2 package (Wickham 2009).
Introduction Today, I’m looking at section 1.4 of Introduction to Linear Optimization. The goal of this section is to find “useful geometric insights into the nature of linear optimization programming problems”. I will recreate the examples from the book in R.
In the following examples, we want to visually examine linear programming problems in order to:
See what the objective function being optimized looks like Visualize the feasible set based on the given constraints If possible, visually identify solution.