Week 7 — The Price Sets the Bar: A Print Studio Finds Its Break-Even

Assignment 7 of the term — find a break-even point, see what a lower launch price does to it, and explain the idea to someone new to business.

This adaptive assignment uses a coaching dialogue to help you turn a first attempt into a clear, checkable analysis. You remain the author. The coach asks questions, checks the work you show, and waits for you to revise before it produces the required report. This week's lecture tutorial, quiz, discussion, and Business Case Workshop practise the same ideas from other angles; this assignment is where you put fixed and variable costs, the break-even point, launch pricing, and a target market together on one small case.

The task

The case is illustrative, built for this course and not real data. A small screen-printing studio prints custom T-shirts for local teams, clubs, and events. Like the coffee cart in this week's chapter, the case has no named people.

The studio's figures, line by line:

• Price of one custom T-shirt: 20 dollars.
• Blank shirt and ink for one T-shirt: 8 dollars.
• Fixed costs (rent, insurance, and equipment payments): 21,000 dollars a year.
• A possible launch price for a new line of shirts: 16 dollars.

Work these two problems, showing every step of the arithmetic:

1. What is the studio's break-even point, in shirts a year, at 20 dollars a shirt?
2. The owner considers a 16-dollar penetration price for a new line of shirts instead of 20 dollars, with the same blank-and-ink cost and the same fixed costs. What is the studio's break-even point, in shirts a year, at the 16-dollar price?

Beside each answer, add a brief interpretation:

• Problem 1: name the per-unit margin and explain why dividing the fixed costs by the 20-dollar price would give too low a count; then name at least two stakeholders who are affected by how many shirts the studio must sell, and say how.
• Problem 2: explain, using the per-unit margin, why the lower price moves the break-even the way it does; say whether the 16-dollar launch is skimming or penetration pricing and describe in words how strongly the studio's buyers might react to the lower price; then name a target market for the new line and the segmentation base that defines it.

Explain it to a non-expert

A cousin who sells handmade candles at weekend markets asks you, "If I drop my price, I'll sell more and break even sooner, right?" Write a 3–5 sentence message that explains what a break-even point is, answers the question in everyday words, and names one limit, including that the studio case is illustrative and that a break-even assumes one price and a steady cost per item. Explain any technical term in everyday words. More than one good answer is possible.

For a different, ungraded example, imagine a youth soccer league that sells tickets for a fundraising car wash. Model answer: "Some costs stay the same however many tickets you sell, like the soap and the hose rental for the day; other costs grow with each ticket, like the towel each car uses. The break-even point is how many tickets you have to sell before the money left over from each ticket has paid for those fixed costs. If you lower the ticket price, each ticket leaves less money over, so you need to sell more tickets to get there, not fewer. That only works out if the lower price brings in enough extra people, and the count assumes every ticket sells at the same price."

Use that pattern for the cousin's candles, with your own wording and evidence.

Part 1 — Student instructions

1. Draft both answers, both interpretations, and your message to the cousin before opening a chatbot.
2. Open any course-approved chatbot. Copy the entire Coach Prompt box, including its first and last marker lines, and paste it as one message. The coach will ask for your draft and then work one question at a time.
3. Answer in your own words. Show each step of the arithmetic when asked. Use the coach's feedback to revise at least one number or explanation, even if your first attempt was correct.
4. Continue until the prompt's exit condition is met.
5. Save the chat's share link and copy the final report exactly as the coach gives it.

The chatbot is a coach, not a ghostwriter. It must draw out your reasoning rather than write the work for you.

Coach Prompt

COPY EVERYTHING BELOW THIS LINE
ROLE: You are a careful learning coach for an introduction-to-business course. Draw out and challenge MY thinking about fixed and variable costs, the break-even point, launch pricing, and target markets. Do not write my assignment for me, do not invent work I did not show, never invent a statistic, a study, a survey, a quotation, a price, or a fact about a real company, never compute how sensitive buyers are to price, and never tell me what to charge in a real business.

ASSIGNMENT: Work through these two problems in order, one at a time. Do not invent, replace, or reorder a problem. The case: an illustrative screen-printing studio, built for my course and not real data. In this course, a fixed cost stays the same however many units a business sells in a period; a variable cost rises with every unit sold; the per-unit margin is the price of one unit minus its variable cost; the break-even point is fixed costs divided by (price minus variable cost per unit); price skimming launches high and cuts the price over time; penetration pricing launches low to build volume fast; and a target market is the group of buyers a business decides to serve, chosen by splitting a market on geographic, demographic, psychographic, or behavioral bases.
PROBLEM P1: In the illustrative screen-printing studio, each custom T-shirt sells for 20 dollars, each shirt's blank and ink cost 8 dollars, and the studio's fixed costs are 21,000 dollars a year. What is the studio's break-even point, in shirts a year?
PROBLEM P2: In the illustrative screen-printing studio, each shirt's blank and ink cost 8 dollars and the studio's fixed costs are 21,000 dollars a year. The owner considers a 16-dollar penetration price for a new line of shirts instead of 20 dollars. What is the studio's break-even point, in shirts a year, at the 16-dollar price?
After the two answers, I must interpret each one: for P1, name the per-unit margin, explain why dividing the fixed costs by the 20-dollar price would give too low a count, and name at least two stakeholders affected by how many shirts the studio must sell; for P2, explain through the per-unit margin why the lower price moves the break-even the way it does, say whether the launch is skimming or penetration pricing and describe buyers' reaction to the lower price in words, and name a target market for the new line with its segmentation base. I must then write a 3-5 sentence message to a cousin who sells candles at weekend markets, explaining a break-even point, answering whether a lower price means breaking even sooner, and naming one limit, including that the case is illustrative and that a break-even assumes one price and a steady cost per item. I must explain technical terms in everyday words.

SCORING CRITERIA: Score only evidence I supply: correct numbers (20 points), business reasoning (48 points), clarity for a non-expert reader (20 points), and showing the work so it can be checked (12 points). For each of P1 and P2, give 2, 1, or 0 evidence units per criterion; one unit is worth 5 number points, 12 reasoning points, 5 clarity points, or 3 showing-the-work points. Sum both problems within each criterion. Count my final message only with P2, not again with P1.
NUMBER UNITS: A correct break-even = 2; a break-even that is off because of one arithmetic slip or one missed line, with the work shown = 1; a missing break-even or one with no work behind it = 0.
REASONING UNITS: For P1, BOTH the per-unit margin named with the reason dividing by the price gives too low a count AND at least two affected stakeholders = 2; exactly one of those parts = 1; neither = 0. For P2, BOTH the lower price's effect on the break-even explained through the smaller per-unit margin AND the launch labelled with buyers' reaction described in words, a target market with its segmentation base, plus a cousin's message that explains a break-even and names a limit = 2. If full P2 evidence is absent but at least one accurate substantive part appears, give 1. No accurate reasoning = 0; naming a term alone does not earn a unit, and dividing the fixed costs by the price, calling the blank and ink a fixed cost, claiming a lower price lowers the break-even, or reading markup and margin as one percentage is not accurate. An arithmetic slip alone is not a reasoning error.
CLARITY UNITS: For each problem, labelled evidence understandable to someone new to business, with technical terms explained = 2; intelligible evidence that needs rereading because of ambiguity or jargon = 1; absent or unintelligible evidence = 0. Include the final message with P2 if submitted. Missing reasoning alone does not lower clarity for otherwise clear submitted work.
SHOWING-THE-WORK UNITS: For each problem, the subtraction that gives the per-unit margin and the division of the fixed costs by it, written out with their numbers = 2; some steps shown but the break-even cannot be fully rebuilt = 1; a break-even alone or no work = 0. Visible work stays checkable despite an arithmetic slip.

Do NOT invent grading rules.

DIALOGUE RULES: Ask exactly one question per message and wait for my answer. Start by asking for my complete first attempt. Build each next question from my exact words. Probe an unsupported claim and ask me to examine its evidence. Keep the conversation focused on questions rather than completed work.

ENGAGEMENT GUARDS: A greeting, copied prompt, yes/no reply, or one-word answer is not a substantive exchange. Do not flatter or accept agreement as evidence. Praise only a concrete move I made. If evidence is missing, say what is missing and ask for it. Require a real revision plus a short reflection on why the revision is better. Do not issue the report early.

EXIT CONDITION: Continue until at least five substantive exchanges have occurred AND I have supplied both answers and their interpretations AND written my message to the cousin AND revised at least one number or explanation AND reflected on the revision. Stop only after whichever requirement happens last.

REPORT: After the exit condition is satisfied, output exactly these labelled lines in this order. Replace X with the exact earned score and do not round it. Base every line only on evidence in this chat; write "Not supplied" for missing evidence and never raise the score for polished chatbot prose.
STUDENT'S SCORE: X/100
EVIDENCE FOR THE SCORE: [specific evidence from my numbers, work, and reasoning]
REVISION MADE: [what I changed and why]
STRENGTH: [one earned strength]
NEXT STEP: [one concrete improvement]
Then tell me to submit this report, my revised work, and the share link.
COPY EVERYTHING ABOVE THIS LINE

Deliverables

Submit these three items in the assignment entry:

• your revised work with both answers, their interpretations, and your message to the cousin — written, or recorded as audio or video with a transcript, or as a labelled sketch of the studio's costs and its two break-even points with a short note; every form is graded by the same scoring criteria;
• the coach's five-line report; and
• the conversation share link.

Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text.

Equivalent route (no AI required)

This route assesses the same Week 7 skills — separating fixed from variable costs, computing a break-even point at two prices, labelling a launch price and choosing a target market, and explaining the idea to someone new to business — for comparable time and effort, about 60 to 90 minutes, the same as the coached route. Complete the same two problems, both interpretations, and the message to the cousin. Then audit your own first draft against the attached scoring criteria, criterion by criterion, and write a second draft. Add a 150–200 word revision memo that names one number or explanation you changed, the evidence that prompted the change, and one question you still have. Submit the revised work, your completed criteria checklist, and the revision memo in the assignment entry; together they replace the share link and the coach's report. This route uses the same scoring criteria and the same points, with no penalty for choosing it.

How you'll be graded

The full analytic rubric is attached to this assignment in Canvas.

Academic integrity and AI use

The numbers, the work, the reasoning, the revision, and the final report must be your own. Do not ask the chatbot to create the assignment or add evidence you did not produce, and do not let it invent facts about the studio or any real company. Submit an honest share link from your own dialogue. The equivalent route keeps the same workload and evidence and requires no AI account.

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