Calzones vs. Mini-Pizzas -- A Linear Programming Problem
This material was originally developed by
Spreadsheets Across the Curriculum as part of its collaboration with the
SERC Pedagogic Service.
Initial Publication Date: July 18, 2007
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.
- 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.
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Assessment
The end-of-module questions can be used for assessment.
The instructor version contains a pre-test.