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Animal feed mix problem

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

The animal feed mix problem determines ingredient proportions that satisfy nutritional constraints while minimizing feed cost.

The animal feed mix problem finds ingredient proportions that satisfy nutritional limits while minimizing the cost of one kilogram of feed. Because its objective and constraints are linear, it is a linear programming problem; blending applications can also involve mixed integer linear programming. section 2.1.4

A three-ingredient formulation uses:

  • Corn, limestone, and soybean meal as nonnegative decision variables whose proportions sum to one. section 2.1.4
  • A cost objective of 30.5x1 + 10x2 + 90x3, minimized subject to calcium, protein, and fiber requirements. section 2.1.4

Worked feed mixture

The reported solution contains 65% corn, 3% limestone, and 32% soybean meal, with a total mixture cost of $0.4916 per kilogram.

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

How deep it goes
Formulates variables, objective, nutritional constraints, and a PuLP implementation, but does not explain solver internals.
Examples
Uses corn, limestone, and soybean meal with calcium, protein, fiber, cost, and solved percentage values.
What it assumes
Assumes familiarity with linear objective functions and constraints while defining the feed formulation concretely.
What you can do after
Apply it via PuLP to build, solve, and inspect a linear feed-mixing model.
How it connects
Connects linear programming with blending problems, mixed integer linear programming, and mathematical optimization libraries.
Cover of Optimization Algorithms: AI techniques for design, planning, and control problems
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