# Calzones vs. Mini-Pizzas -- A Linear Programming Problem

This material is replicated on a number of sites as part of the SERC Pedagogic Service Project

#### Summary

This module presents a linear programming problem. An example of the revenue-maximizing product mix for a pizza parlor is developed. This is an example of a more general mathematical optimization (maximization or minimization) problem. The applications of linear programming to a wide variety of areas are also discussed. The focus of the module is on linear equations and linear inequalities, and solving the optimization problem by examining the vertices and facets of the feasible set and the slope of level curves of the objective function.

## Learning Goals

Students will:
• Graph level curves of the objective function of a linear programming problem.
• Alter parameter values of the level curves and analyze the effects of such changes on the slope of level curves.
• Determine whether particular values of the choice variables are feasible.
• Use a simple (albeit inefficient) algorithm to determine a solution to the linear programming problem.
In the process the students will:
• Distinguish between maximization and minimization problems.
• Use graphs to visualize the feasible set of a linear programming problem.
• Learn the effects of changing parameter values on the solution to linear programming problems

## Context for Use

This module is appropriate for a wide variety of activities in applied mathematics, decision sciences, and economics. The example developed in the module is a simple product-mix problem, but the technique can be applied to a wide variety of situations.

## Description and Teaching Materials

SSAC2006.HB71.JMP1.2-stdnt (PowerPoint 153kB Jul19 07)

The module is a PowerPoint presentation with embedded spreadsheets. If the embedded spreadsheets are not visible, save the PowerPoint file to disk and open it from there.

This PowerPoint file is the student version of the module. An instructor version is available by request. The instructor version includes the completed spreadsheet. Send your request to Len Vacher (vacher@usf.edu) by filling out and submitting the Instructor Module Request Form.

## Teaching Notes and Tips

The module is constructed to be a stand-alone resource. It can be used as a homework assignment or lab activity. It can also be used as the basis of an interactive classroom activity.

## Assessment

The end-of-module questions can be used for assessment.

The instructor version contains a pre-test.