Showed up right on time today. We’re getting our first tests back. Looks like I wasn’t alone in not finishing the test. Question 11 was omitted because only two people in the class got it right. Got 75%, which is lower than I hoped, but not lethal. I was expecting to end up in the 80% range. I missed one very simple problem, just giving the dimensions of a matrix. There’s no excuse for that; I transposed the dimensions. Had I gotten that one right, I would have been solidly at 85%. Have to be more careful next time. In general, I’m going to have to step up my performance, but it’s not yet time for panic.
Back to maximizing problems and Simplex Method.
Steps to solving a miximizing problem:
- Put the problem in standard form
- Introduce slack variables and set the linear objective function equal to zero.
- Write the initial simplex tableau.
Pivoting is the method one uses to evaluate the limits of a set of linear equations. The limits, in this case, are what would have been the corner points in a two-dimensional graph of inequalities. The limit or corner points are the extreme point in each direction.
To pivot a matrix is to apply matrix operations to one element of the matrix, called the pivot element, such that the pivot element is equal to one, and all other entries in the same column as the pivot element (called the pivot column) are equal to zero.
Normally the process of pivoting involves dividing the row of the pivot element by the value of the pivot element, and then using conventional row operations to render the other elements in that column zeros.