All about Linear Programming
One application of linear optimization is space allocation and efficient facility usage.Copyright Space Utilization Tool, Technology Transfer Program, NASA https://technology.nasa.gov/patent/LAR-TOPS-107
Students learn about linear programming (also called linear optimization) to solve engineering design problems. As they work through a word problem as a class, they learn about the ideas of constraints, feasibility and optimization related to graphing linear equalities. Then they apply this information to solve two practice engineering design problems related to optimizing materials and cost by graphing inequalities, determining coordinates and equations from their graphs, and solving their equations. It is suggested that students conduct the associated activity, Optimizing Pencils in a Tray, before this lesson, although either order is acceptable.
In order to design the best solution to a problem, engineers frequently aim to maximize the quantity of a particular design element (such as a material) or minimize a quantity (such as cost). To do this, they design within a set of constraints that are sometimes given by the client and other times simply the limitations of the amounts and types of available resources. During the engineering design process, it can be helpful to predict the expected outcomes of different approaches before creating and testing prototypes. While not every situation is suitable for quick and accurate prediction, certain scenarios are ideal. For instance, when every constraint can be fit to a linear mathematical model, then a technique known as “linear programming” can be used to find the optimum solution. Examples of engineering applications of linear programming include optimizing the energy use cost in a building system analysis, material analysis of a truss, and space optimization in city planning, office design and grocery store shelves.
After this lesson, students should be able to:
- Describe linear programming as finding the “best” solution to a problem.
- Define and apply the following engineering design terms: constraint, feasible, optimize.
- Use linear programming to solve example real-world engineer design problems.