Operations research
Explainer
Linear Programming: Optimising Under Constraints
A mine can't dig everywhere at once. Linear programming picks the best plan.
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Lesson notes
Key points
- Linear programming chooses values of decision variables to maximise or minimise a linear objective function.
- Constraints are linear inequalities, like limited truck hours or plant capacity, that restrict which plans are allowed.
- Every plan satisfying all constraints together forms the feasible region, and the optimum lies inside it.
Definitions
- Linear programming
- Optimising a linear objective subject to linear equality or inequality constraints on decision variables.
Takeaway: LP optimises a linear objective within a feasible region.
Quick check: What is the set of plans meeting all constraints called?
- Objective function
- Feasible region
- Slack set
Objective functionConstraintsFeasible region
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