We exploit the symbolic manipulation capability of Mathematica to elucidate the simplex algorithm of linear programming clearly and intuitively. We then develop a set of tools for conducting sensitivity analysis of the optimal solution. In order to utilize Mathematica's efficient linear programming routine, we develop a function which can deduce the final tableau from the Spartan output of ConstrainedMax. This final tableau contains all the information usually provided by a good linear programming package, which can than be explored using the techniques of sensitivity analysis developed in the paper. This enables the package to be applied to a substantive problem, relying on Mathematica's native code for intensive computation. To illustrate, we apply the package to analyse a classic problem in efficient nutrition.