Making the Best Choices

Many designs—bridges, airplanes, even soda cans—require optimizing several variables at once (like cost, strength, weight).

Multivariable Optimization

Using partial derivatives, we find where a function reaches its maximum or minimum. This helps engineers pick the best dimensions and materials.

Constraints and Lagrange Multipliers

Sometimes, there are extra requirements (constraints). The method of Lagrange multipliers helps find the best solutions within these limits.

Real-World Impact

Optimization saves resources and improves safety and performance in countless products.