Lesson 4A: Optimization Basics

Learn how to optimize functions and find minimum/maximum values using mathematical modeling techniques.

Understanding Optimization

What is Optimization?

Mathematical optimization involves finding the best solution from a set of possible options. It's used in economics, engineering, and science.

Key Concepts:

  • Objective functions
  • Constraints
  • Local/Global Extremas

Example Formula

# Example: Maximize Area of Rectangle
# Objective: Maximize A = x * y
# Constraint: 2x + 2y = Perimeter

Optimization Simulator

Objective Function Explorer

Adjust variables in the visualizer to see how different parameters affect optimization results.

Launch Full Tool

Apply What You've Learned

Problem 1

Find the dimensions of a rectangle with maximum area if its perimeter is fixed at 40.

Problem 2

What's the maximum value of the function f(x) = -x² + 5x between x=0 and x=5?