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.
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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?