Optimization
Optimization is finding the best place, amount, or setup to get the most out of what you have.
When you arrange fruit in a bowl, you try different spots to fit the most pieces without stacking them. Moving the largest pieces to the center and smaller ones to the edges lets you fit more in the same space. That setup is the optimal solution — the one that gives you the best result with what you have.
Explaining optimization by grade level
Think about placing a tall tower so phones work for the most people. You want it where lots of people live. If you put it too far away, calls drop. Picking the best spot is optimization.
Projects that explore optimization
Can math find the best spots to build cell phone towers? In this project, each possible tower location in Kern County gets an optimization value based on population density and highway traffic. Three different models emerge from the math: one picks the most profitable spots with fewer towers, another spreads towers out for the widest coverage, and a third balances profit and coverage. Comparing these setups reveals how different goals change which arrangement counts as best — and adjusting for population growth shows how those ideal locations shift over time.
Finding the best place to build a gas-powered plant in Southern California means weighing several competing factors at once. You place a coordinate grid over a map and score each candidate location based on distance to cities, power loss during transmission, and environmental and property costs. An objective equation combines these factors to rank every spot. The model points to a location about 50 miles east of Lancaster as optimal — though during high summer demand, two locations closer to Los Angeles also become feasible. That shift shows how changing conditions can reshape which choice counts as best.