Required materials

Each student will require 12 large Lego blocks (rectangular top with 8 connectors) and 18 small Lego blocks (square top with 4 connectors).

Audience

This module is designed with Linear Algebra students in mind. However, the module may be adapted to students with exposure to linear systems in the context of a College Algebra course by restricting the focus to problems with two variables.

Required knowledge

• Linear equations describe lines, planes, or hyperplanes (depending on the dimension
• Linear inequalities describe half-spaces bounded by lines, planes, or hyperplanes (depending on the dimension)
• Linear independence of equations
• The solution to a system of n linearly independent equations defines the point of intersection of the lines/planes/hyperplanes described by the equations

Objectives

1. Introduce constrained optimization through an engaging activity
2. Introduce linear optimization modeling
3. Introduce a geometric algorithm for solving a bounded linear optimization model that (i) reinforces concepts from linear algebra, and (ii) introduces concepts that are fundamental to the study of optimization
4. Provide a teaser for the breadth of problem-types that can be tackled using optimization