Jumping right in.Last section, which I missed, was about converting a minimization problem into a maximization problem.
Conversion of a minimization problem involves turning the matrix of the minimization problem into a dual problem. This requires transposing the rows and columns of the matrix, such that row x, column y becomes row y, column x. The purpose of this, effectively, is to invert the problem into a maximization problem, which can then be solved via simplex method. This inversion can be pictured as reflecting the set of linear equations across the 0,0 point, and then moving it back to the first quadrant of the graph.
Once the maximizing problem is solved, it is converted to the solution for the minimizing problem. The minimum value will be equal to P of the maximizing problem. The X variables of the minimizing problem will be equal to the equivalent slack variables of the maximizing problem.