What price maximises profit at our school bake sale?

AA SLAI SLAA HLAI HL Solid Also in: Calculus, Statistics

Research question

Using a demand curve estimated from a survey of students, what price maximises profit for [a product], and how does the optimum change if costs rise?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

A real sale gives you real decisions. Estimating demand from survey data, building cost and revenue functions, and optimising with calculus is a textbook topic done with your own data — and you can test it at the next sale.

The mathematics you'll need

Linear or exponential demand models from survey data
Revenue R = pq and profit P = R − C
Differentiation to maximise profit
Price elasticity (optional)

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Survey 60+ students on the most they would pay; record actual costs of ingredients and packaging.

Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Design the survey carefully (avoid leading questions).
Fit a demand model.
Build revenue and profit functions and maximise.
Test the price at a real sale if possible.
Reflect on survey honesty and sell-outs.

Pitfalls that cost marks

Leading survey questions.
Ignoring fixed costs.
Treating stated willingness to pay as real behaviour.

Showing personal engagement

Run the sale and compare predictions with sales.
Compare two products.
Reflect on how you would change the survey.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Model demand with two variables (price and portion size) and discuss the trade-off.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).