Quantitative Analysis for Management, 13/e

M7.1 How to Set Up the Initial Simplex Solution

Let us consider the case of the Flair Furniture Company from Chapter 7. Instead of the graphical ­solution we used in that chapter, we now demonstrate the simplex method. You may recall that we let

$$\begin{array}{c}T=\text{number} \text{of} \text{tables} \text{produced}\\ C=\text{number} \text{of} \text{chairs} \text{produced}\end{array}$$

and that the problem was formulated as

$$\begin{array}{llllll}\text{Maximize profit}\hfill & =\hfill & \$70T\hfill & +\hfill & \$50C\hfill & \left(\text{objective function}\right)\hfill \\ \text{subject to}\hfill & 2T\hfill & +\hfill & 1C\hfill & \le \hfill & 100\hfill & \left(\text{painting hours constraint}\right)\hfill \\ 4T\hfill & +\hfill & 3C\hfill & \le \hfill & 240\hfill & \left(\text{carpentry hours constraint}\right)\hfill \\ T,C\hfill & \ge \hfill & 0\hfill & \left(\text{nonnegativity constraints}\right)\hfill \end{array}$$

Converting the Constraints to Equations

The first step of the simplex method requires that we convert each inequality constraint (except nonnegativity constraints) in an LP formulation into an equation.1 Less-than-or-equal-to constraints $(\le )$ such ...