LP Applications

Optimization · Axiom Academy

Discover how Linear Programming optimizes everyday decisions. A nutrition planner needs to minimize food costs while meeting daily vitamin requirements. Adjust the servings to see how costs and nutrients change. A company has two warehouses and needs to ship products to three stores. Each route has different costs. Click on routes to explore different shipping strategies. A factory can produce Product X or Y each day. Each has different profit and production capacity. Adjust the weekly schedule to maximize profit. An investor has 100,000 to allocate between stocks and bonds. Adjust the allocation to explore the risk-return tradeoff. All four problems share the same mathematical structure. That's why they're all Linear Programming problems! Each problem optimizes (minimize or maximize) a linear combination of variables: cost, profit, shipping fees, or returns. All restrictions are linear equations or inequalities: nutrient requirements, supply limits, capacity bounds, or budget constraints. Decision variables must be non-negative: you can't have negative servings, shipments, production, or investments. Linear Programming problems can be solved efficiently even with thousands of variables using algorithms like the Simplex method or interior-point methods.

This is the written version of the interactive lesson above. See the full Optimization course.