What is Linear Programming?

Optimization · Axiom Academy

INTRO What is Linear Programming? Discover how businesses optimize decisions with limited resources. You own a factory that makes chairs and tables. Use the sliders to decide how many of each to produce. Step 2: The Straight-Line Nature Notice something special: all relationships are linear. Adjust the sliders to see how profit grows in a straight line. Let's visualize ALL possible production plans. The shaded area shows every valid combination of chairs and tables. Click anywhere in the graph to test a production plan! Here's the magic: the best solution is ALWAYS at a corner! Click on each corner to see the profit. Now that you've explored the intuition, here's the mathematical framework. A linear function to maximize (or minimize). In our example: maximize 50c + 80t. Linear inequalities that define the feasible region. In our example: 2c + 3t ≤ 100 (wood), c + 2t ≤ 80 (labor). In the 1940s, "programming" meant planning or scheduling. Linear programming = planning with linear constraints. Not related to computer programming!

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