Business Optimization

Algebra 1 · Axiom Academy

Business Optimization: The Most Profitable Plan Limited cocoa, limited time — a system of inequalities draws the line between the plans you can make and the one that earns the most. You run a small chocolate shop selling boxes of truffles ( x ) and caramels ( y ). Each truffle box earns 10 , each caramel box 8 — but you only have 180 g of cocoa and 100 minutes of work today. Which mix of boxes makes the most money? Drag the sliders to pick a plan. The shaded region is every plan you can actually make — your point glows green inside it and turns red the moment you run out of cocoa or time. Hunt for the biggest profit you can reach. Here's the shortcut that runs all of business optimization: the best plan is always a corner of the region. Click each corner to read its plan and profit, then find the one that pays the most. The winning plan is 40 truffle boxes and 30 caramel boxes for 640 — and it sits exactly where the cocoa and time limits cross. That's linear programming : graph the constraints, find the corners, and the best plan is always one of them. The same move schedules airlines, blends fuels, and routes deliveries.

This is the written version of the interactive lesson above. See the full Algebra 1 course.