Week 3 exercises
Footprint, life cycle cost and cost per tonne for Test 2 · Heizer S5
These are the three kinds of questions planned for a Week 3 bonus sheet, which was not written in class; here they are exercises with answers. Test 2 (Week 4, 22 October) asks calculations of these kinds, with changed numbers; cost per tonne comes up as in the Backhaus Kaya case (what Test 2 asks). Work on paper, with a calculator; write the unit next to every result.
The formulas in words. Footprint = Σ amount × emission factor, stage by stage; the amount must be in the factor’s unit (kg, kWh, tonne-km). Share of a stage = stage ÷ total × 100 %; the biggest stage is the hotspot. Tonne-km = tonnes moved × km. Life cycle cost (Equation S5-2) = purchase price + energy cost per km × km per year × years + other operating cost per km × km per year × years. Crossover in km = difference in purchase price ÷ difference in cost per km; in years = crossover km ÷ km per year. Cost per tonne avoided = extra cost per year ÷ tonnes CO₂e saved per year (minus = the measure saves money). Cheapest-first plan: sort the measures by € per tonne and add them, cheapest first, until the target is reached.
Before you hand in, check three things: ① every result with its unit, “x [unit] per [unit]” · ② round trips, crates and people up · ③ every decision in words, matching your numbers.
Formula sheet to download: Week 3 formula sheet: footprint, life cycle cost, break-even, € per tonne (PDF, 1 page) — the one-page sheet handed out with the bonus sheet; print it and keep it next to you while you practise.
Start here: Example S2 (Blue Star) and Solved Problem S5.2 (school buses) in Supplement 5 of Heizer et al. (2023), then the warm-up sheet and the Colab footprint planner from Thursday.
Three sets of three exercises with answers appear here after Thursday’s class: footprint, life cycle cost and cost per tonne.
Sources
Heizer et al. (2023), Supplement 5 (Equation S5-2, Example S2, Solved Problem S5.2). Exercises: own material, R. Bartnik (2026); illustrative factors and prices.