📅 The Simplex Method - In Excel

Abstract

We will look at mechanizing the Simplex Method in Excel

Using the Excel Solver Add-In

Let us take the same problem as before:

\[ Maximise\ 7.75x_1 + 10x_2 \\ \] \[ Subject\ to \\ \begin{cases} C1: -3x_1 + 2x_2 &<= 3 \\ C2: 2x_1 + 4x_2 &<= 27 \\ C3: 9x_1 + 10x_2 &<= 90 \\ x_1, x_2 >= 0 \end{cases} \]

Procedure

1. Set up an Excel sheet as shown in the picture below. We enter in the objective function and the constraints in tabular form as shown:

2. Next we invoke the Solver Add-in: (Data -> Solver):

3. We set up the Solver for our problem as follows: Hit the SOLVE button.

4. Choose to have all the three kinds of Reports from Solver (Answers, Sensitivity, and Limits).

This will create three new tabs which give additional information on:
- How “centered” the solution is, or is it sensitive to variations of some parameters
- How much slack do the individual constraints still have, at the end

We will discuss this in class!

The complete Excel file is here for your reference.