Why compute the break-even output?

It marks the volume at which two sites cost the same, so the choice either side of it differs; a unit-cost comparison alone hides that.

Is payback enough to judge an environmental investment?

No: compliance costs, penalty risk and brand value also count, and payback is only a financial threshold.

S5 Geography | Industry and Manufacturing Paper 3 (Site Choice and Sustainable Industry)

2026-11-04

Tutor Prep Guide · Secondary Geography

Site choice is a total-cost question: fixed and variable costs belong in the same account, which yields a break-even output. Sustainability then turns emissions, water and payback into numbers.

Attempt first, mark afterwards　Allow about thirty minutes; write the formula first, then check units such as kilograms against tonnes and litres against cubic metres.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10 items
Suggested time	About 30 minutes
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: S5 Geography \| Industry and Manufacturing
Level	S5 (Secondary 5) Geography

02　Questions (10 items)

FoundationSite A costs 2,400,000 fixed plus 18 per unit; site B costs 1,200,000 fixed plus 26 per unit. At 200,000 units a year, which is cheaper and by how much?
FoundationFor the same two sites, which is cheaper at only 100,000 units a year, and by how much?
FoundationAt what output do the two sites cost the same, and which should be chosen above that output?
FoundationA plant uses 1,200,000 kilowatt-hours a year and each unit emits 0.7 kilograms of carbon dioxide. How many kilograms and tonnes is that?
IntermediateIf rooftop solar cuts the plant carbon emissions from electricity by 25 per cent, how much is avoided and what remains?
IntermediateA plant discharges 3,000 cubic metres of wastewater a day at a pollutant concentration of 200 milligrams per litre. How many kilograms are discharged, and how much remains after 80 per cent removal?
IntermediateEnergy-saving equipment costs 900,000 and saves 180,000 a year. What is the payback period, and what annual saving would be needed to pay back within three years?
ChallengeA plant produces 480,000,000 of output on 12 hectares. What is output per hectare, and what does it fall to if the site grows to 15 hectares with output unchanged?
ChallengeA plant recycles 35 per cent of its 3,000 cubic metres of wastewater a day, with water at 6 dollars a cubic metre. How much is saved daily and yearly over 365 days?
Error redoA student compares only variable cost per unit and concludes the lower one is always cheaper. What is wrong?

03　Answers and one-line notes

#	Answer	One-line note
1	Site A at 6,000,000, cheaper than site B by 400,000.	Site A is 2,400,000 plus 18 times 200,000, giving 6,000,000; site B is 1,200,000 plus 26 times 200,000, giving 6,400,000; the gap is 400,000.
2	Site B at 3,800,000, cheaper than site A by 400,000.	Site A is 2,400,000 plus 18 times 100,000, giving 4,200,000; site B is 1,200,000 plus 26 times 100,000, giving 3,800,000. Low fixed cost wins at low volume.
3	Break-even at 150,000 units; above it, site A.	The fixed cost gap 2,400,000 minus 1,200,000 over the unit cost gap 26 minus 18 gives 150,000 units; site A has the lower variable cost, so it wins at high volume.
4	840,000 kilograms, which is 840 tonnes.	1,200,000 times 0.7 gives 840,000 kilograms; dividing by 1,000 gives 840 tonnes.
5	Two hundred and ten tonnes avoided, leaving 630 tonnes.	840 times 25 per cent is 210 tonnes, and 840 minus 210 leaves 630 tonnes. Cutting a share only means something against a stated baseline.
6	600 kilograms before treatment and 120 kilograms discharged afterwards.	3,000 cubic metres is 3,000,000 litres; times 200 milligrams gives 600,000,000 milligrams, or 600 kilograms; the remaining 20 per cent is 120 kilograms.
7	Five years; three-year payback needs 300,000 a year.	900,000 divided by 180,000 is five years; 900,000 divided by three is 300,000, so the present scheme misses a three-year target.
8	40,000,000 per hectare, falling to 32,000,000 at 15 hectares.	480,000,000 divided by 12 gives 40,000,000; 480,000,000 divided by 15 gives 32,000,000, a fall of 20 per cent in land efficiency.
9	1,050 cubic metres reused, saving 6,300 a day and 2,299,500 a year.	3,000 times 35 per cent gives 1,050 cubic metres; times 6 dollars gives 6,300 a day, and times 365 gives 2,299,500 a year.
10	Fixed cost is ignored: at low volume the low fixed-cost site is cheaper, and only above the break-even output does the low variable-cost site win.	Site A is cheaper per unit at 18 dollars but carries 2,400,000 of fixed cost; site B costs 26 per unit on only 1,200,000 of fixed cost. At 100,000 units site B totals 3,800,000 against 4,200,000 for site A.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

Need a tutor for this chapter? Register here Tutor Registration →

Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.