Teacher Guide

$0.03 x 1,000 x 52 = $1,560 a year. Three cents is not a small number once it is multiplied by everything. Students who reach a figure in the thousands have understood the point.

Making more spreads fixed costs thinner, so the obvious answer is make thousands. The two real limits are that unsold stock is money thrown away, and that you have to pay for materials before anyone buys anything.

The big pack is $0.12 a sticker against $0.15, so cheaper per sticker. What they need to know first: whether they will use 200, whether they have $24 now, and whether stickers spoil. Cheaper per unit is not automatically better.

$2.00 x 10 = $20.00 against $0.80 x 40 = $32.00, so the second product wins on total margin. What would change it: how long each takes to make, and whether you could actually sell 40.

Cutting the sign from $9.00 to $3.00 removes $6.00 of fixed cost, so break even falls by $6.00 / $1.50 = 4 sales. The counter-argument is that a worse sign may cost more sales than it saves, and there is no way to know without trying it. Both halves needed.

Two real ways to find out instead of guessing: ask the week 17 testers what they would pay, or run session one at one price and session two at another, which is exactly what week 33 sets up.

The second stall is the better bet for session 6 because it climbs every session, while the first, though it also rose from 4 to 8, dipped twice on the way. Accept any answer that argues from the shape rather than from the total.

Without the $16 customer, stall B averaged $1.60 over five customers. That is the lesson: an average over a handful of sales can be moved almost entirely by one of them.

Bags make $2.20 each against cards at $1.40. To beat the cards' $19.60 they would need 9 bags instead of 4, so 5 extra. Whether that is realistic depends on how many people will pay $6.00, which the table does not answer.

A business like stall B is anything with occasional big days: an ice cream stall, a stadium seller, a shop near a school on a half day. Owners deal with it by carrying stock that keeps, or by staffing up only on the big days.

$120 shared among five similar stalls is $24 each, less than the $40 even share of the whole room. Ways to be picked that are not price: being first in the walking route, looking better, being the only one with a certain thing, or knowing the customers.

Adding rent, power and the owner's time usually makes a small business look barely profitable. Students who reach 'the owner is paid last' have found something real about small business.

The argument for equal is that it prevents most disputes and nobody tracks hours accurately anyway. The argument against is that it can reward the partner who does least. Students who find the second harder to write have usually noticed it is about a real person in their team.

If they cannot beat the existing solution on price, the two other things are usually convenience and how well it fits this particular customer. Both are real and both are cheaper to compete on than price.

Making the middle option look obvious is done by pricing the cheap one close to it, or leaving out something the customer wants. This is a real technique and noticing it is the whole point of the question.

The page asks for money in per hour: price times how many you could make in an hour. If BEST takes three times as long, it wins only if its price is more than three times GOOD's. Margin per hour is the better measure once costs are known, and week 18 comes back to it.

A high score with no purchases usually means priced too high, or it is nice but they do not need it. Require one reason about price and one that is not.

If no evidence would change their mind, they are not deciding on the numbers. Saying so plainly is the point of the question.

At 1 in 5 waste the cost of 10 is divided by 8 rather than 9, which raises the all-in cost noticeably. The product hurt more is the one with the higher materials cost, because there is more money in each wasted one.

The good sign has to bring in enough extra sales that the extra margin covers $9. At a $1.50 margin that is six extra sales. Whether they believe it is the honest part of the answer.

If the prices are close, most buyers take the better one. Whether that is bad depends on the margins: if the better product also has the better margin, close prices are actively good. Require the arithmetic.

Halfway is half the break-even number, rounded up. If session one lands well below it the realistic responses are to change the price, bring more of the product that sold, or accept a loss. All three are legitimate.

Forecasts run high because people forecast the day they are hoping for, and because they count everyone who walks past as a possible customer. Students who lower their forecast for a stated reason have done the exercise.

At half the forecast, many plans fall below zero. The number that matters is then the break-even figure, and it belongs on the plan in place of the optimistic one.

The 28 not on display are the restock. The rule to write is at what number left on the table somebody puts more out, and it should be well before empty.

A 60 by 45 sheet is 2,700 square centimeters. Any layout with the arithmetic shown is acceptable; the point is noticing that offcuts are money.

The answer to 'how do you know' has to name the measurement and when it was taken. A student who cannot answer it should change the number, not the answer.

The restocking rule should trigger well before the table is empty. A stall that looks picked over sells more slowly than one that looks full, which is worth saying out loud.

A slow stretch with high traffic is a selling problem. A slow stretch with low traffic is a timing problem. Different fixes, and students who separate them are doing real analysis.

Three real reasons the counts disagree: a sale marked in the wrong row, a sale not marked at all while busy, and a miscount at opening. Only the last is carelessness rather than the normal friction of a busy table.

A perfect forecast from a first-time forecaster is luck. Reliable accuracy comes from having been wrong and adjusted, which is why the exercise needs the forecast to have been written in pen.

Slices can disagree, and the resolution is usually that they are measuring different things. Students who find a way for both to be true are doing genuinely good reasoning.

Sales per person who walked past controls for a busier session. Students who reach that on their own have understood the difference between a result and a fair comparison.

A change can work while the session is still worse, if something else got worse at the same time. Naming that in advance stops a wrong conclusion in week 35.

One session is not proof. Any answer above about three sessions with reasoning is good. What matters is that they see a single result as weak evidence rather than as an answer.

What a business that ran twice knows is whether a change did anything, which a business that ran once cannot know about itself. A third session would start to separate a real effect from a good day.