Linear programming and the cheapest diet: a maths EPQ idea
A title to start from
Can linear programming design the cheapest healthy diet, and should we trust its answer?
Why it works as an EPQ
An optimisation technique you can learn independently, applied to a problem with an obvious human check on the answer.
Scope and difficulty
Solid. Solid. A few foods and nutrients by hand, more with a solver.
The maths
Builds on these A Level topics: Algebra and functions · Coordinate geometry.
You would learn:
- Linear programming
- The simplex method (Decision Maths)
- Sensitivity analysis
One possible plan
- Set up a small version with two foods and solve it graphically.
- Scale up with a spreadsheet solver.
- See how the answer changes when prices or constraints change.
- Evaluate why the optimal diet may be one nobody would eat.
Pitfalls
- Nutrition targets with no reliable source.
- Trusting solver output you cannot interpret.
Where to start reading
- Search for: Stigler diet problem linear programming
- A Decision Maths textbook chapter on linear programming
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