Optimization: feasible choices and competing goals
Formulate objectives and constraints, solve a small linear program, trace constrained gradient updates and qualify sensitivity and preference claims.
Choose any lesson or try the project first. Shared lessons retain the same saved work wherever you enter them. Completing a lesson records participation; practice, transfer checks and independent reasoning remain separate.
Recommended preparation and ways to catch up
- Read linear graphs, percentages and basic algebra.
- Shared slope/gradient activities introduce local change before constrained updates.
Find a foundation course · Open contextual refreshers. Each investigation includes a short recap; preparation never locks access.
Loading local course progress…
Your units and lessons
Choose a unit to see its lesson sequence. Every lesson opens on its own page.
Objectives and feasibility
Separate a preferred score from the allowed region.
Build the largest enclosure
Which rectangle gives the most space for a fixed fence?
Optimize within a feasible polygon
Why can checking a few vertices solve this linear production problem?
Local change and constrained search
Trace gradients, step sizes and projection without claiming universal convergence.
Use a slope to improve a choice
When does following the downhill direction overshoot?
Follow a gradient through a computation
Connect a derivative, chain factors, partial gradients and a numerical check.
Descend without leaving the allowed region
Can a constrained minimum have a nonzero derivative?
Sensitivity and multiple goals
State where a resource price applies and make preference assumptions explicit.
Price one more unit of capacity
When does a local marginal value stop predicting a larger change?
Choose between cost and quality
Which options can be rejected without choosing a preference weight?
Defend a feasible resource decision
Formulate a small planning problem with an explicit feasible set, compare exact or enumerated and iterative solutions, test a resource change and explain competing goals. Supply an artifact that a reviewer can recompute.
Build from lesson evidence, compare alternatives, write an artifact, and tackle unfamiliar numerical cases. Use the rubric with a teacher, peer or colleague to assess the quality of your reasoning.
Open the course project