liveBook · Manning

Linear programming

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

An optimization problem with a linear objective function and linear constraints.

Linear programming (LP) finds the best value of a linear objective function while satisfying linear constraints. It models planning and design decisions by representing unknown quantities as decision variables, expressing costs or benefits as an objective, and encoding requirements as inequalities or equalities. section 2.1.4 section 2.5

Animal feed mix

Choose proportions of corn, limestone, and soybean meal to minimize cost while meeting calcium, protein, fiber, non-negativity, and conservation requirements. A PuLP formulation reports 65% corn, 3% limestone, and 32% soybean meal, costing $0.4916 per kilogram. section 2.1.4

A practical LP workflow is:

  • Write the linear objective, choosing minimization or maximization; the feed example minimizes ingredient cost. section 2.1.4
  • Add linear constraints for limits, minimums, maximums, and conservation conditions. section 2.1.4

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

How deep it goes
Defines linearity, works through a feed-mix formulation, and implements it in PuLP without developing solver internals.
Examples
Uses an animal feed mixture with nutrient constraints and references plant layout, wheel design, and finite catenary optimization problems.
What you can do after
Apply it via PuLP by defining variables, objectives, constraints, solving the model, and inspecting the resulting values.
How it connects
Connects linear programming to optimization, objective functions, constraints, mixed-integer programming, and continuous decision variables.
Cover of Optimization Algorithms: AI techniques for design, planning, and control problems
liveBookmanning.com
Read Optimization Algorithms: AI techniques for design, planning, and control problems on liveBook Get the book at manning.com

Also explained in

Compare how 2 books explain linear programming →

Related concepts

This explainer was generated by Manning's knowledge graph from the text of Optimization Algorithms: AI techniques for design, planning, and control problems. The section links point to the parts of the book it draws on.