Managing Your Money: Linear Programming II

Have you ever made decisions about managing your money? Mathematics provides tools that help to make such decisions. One of these tools is linear programming, which helps people choose the best program of action. It Consider the following problem of managing investments in a money market fund and in a bond fund in order to maximize the earnings.

Note: The information below was created with the assistance of AI.

Level of Mathematics
This lesson is designed for:

Upper high school students (Grades 11–12) taking:

Algebra II

Precalculus

Finite Mathematics

Mathematical Modeling

Suitable for college-level introductory linear programming or business math courses.

Students are expected to formulate and solve linear programming problems using algebraic methods and graphical interpretation.

Application Areas
This unit applies mathematics to practical, real-world financial and planning contexts:

Personal Finance:
Investment allocation decisions for maximum return.

Risk balancing between safer and higher-yield investments.

Business & Economics:
Budget optimization and resource allocation.

Return maximization subject to financial constraints.

Operations Research:
introduction to linear programming as a decision-making tool.

Lays groundwork for more advanced modeling tools like software-based optimizers.

Technology & Programming:
References to optimization software (e.g., What’s Best!, Function at Your Best, Finitepak).

Prerequisites
Students should have competency in:

Algebraic expressions and inequalities

Graphing linear equations and interpreting feasible regions

Understanding constraints and objective functions

Substituting coordinates into functions

Basic financial literacy (interest rates, investment types)

Optional but helpful: familiarity with concepts of optimization, constraints, and basic programming logic.

Subject Matter
Core Mathematical Topics

Linear Programming

Identification of decision variables.

Construction of constraints using inequalities.

Determination of feasible regions via graphing.

Evaluation of objective function at boundary points (vertices).

Interpretation of results to guide decision-making.

Applications of Linear Inequalities

Constraints on investment amounts and proportions.

Realistic financial scenarios using money market funds, bond funds, and stock options.

Objective Function Construction

Maximizing return or earnings:

Graphical Analysis

Use of feasible region diagrams to visualize and solve optimization problems.

Exploration of geometric principles behind why optimal solutions occur at vertices.

Critical Thinking & Modeling

Transforming word problems into mathematical models.

Justifying assumptions and interpreting real-world constraints mathematically.

Correlation to Mathematics Standards
Common Core State Standards (CCSS) – High School

Algebra – Creating Equations
HSA-CED.A.1–3: Create equations and inequalities to represent constraints and relationships.

Algebra – Reasoning with Equations
HSA-REI.D.10–12: Graph solutions and interpret feasible regions and systems of inequalities.

Functions – Linear Models
HSF-LE.A.1c: Recognize linear relationships in real-world modeling.

Modeling with Mathematics
HS-M: Use mathematical models to represent and solve real-world problems (finance, investment).

Mathematical Practices

MP1: Make sense of problems and persevere in solving them.

MP2: Reason abstractly and quantitatively.

MP4: Model with mathematics.

MP6: Attend to precision.

MP7: Look for and make use of structure.