Separate refill capacity from display orientation

Write the shop’s actual opening task

A fictional stationery maker supplies boxed stamp sets to a small shop. The sales presentation calls the proposed refill insert ready to display. The shop manager understands that promise to mean opening the outer package and placing the insert on the counter without rearranging the contents. The maker’s designer instead means that the insert keeps the refill sets organized during the handoff. Those are different jobs, even though the same drawing appears in both presentations.

Before discussing capacity, write the shop’s opening task in plain language. The customer should encounter the named product fronts, and the assistant should know whether stock must be transferred into the established counter display. The fictional brief permits that transfer, but it must not be concealed inside a promise of instant presentation. This makes the handling decision part of the design rather than an afterthought left to store staff.

Keep the product assortment unchanged throughout the comparison. All boxes contain the same approved stamp set. Do not solve a layout difficulty by replacing some with smaller samples, omitting accessories or changing the count described on the sales sheet. The point is to choose an honest role for the proposed insert, not to make an attractive drawing win by altering what the retailer receives.

Draw both arrangements before naming the insert

Use centimetres and half-open rectangles [x, x + width) × [y, y + height), inside [0, 10) × [0, 10). Each carton is 6 × 4. Refill permits rotation: A = (0, 0, 6, 4), B = (6, 0, 4, 6), C = (4, 6, 6, 4), D = (0, 4, 4, 6), listing (x, y, width, height). All extents stay inside; intersection areas AB, AC, AD, BC, BD, CD are zero. Display requires the 6-wide facing: use A and E = (0, 4, 6, 4); AE intersection is zero. This establishes two displayed, not optimality. Refill achieves four; area bounds count by floor(100 / 24) = 4. Geometry excludes clearance, height and protection. Check each pair by multiplying positive overlap lengths on both axes.

The supplied calculation was checked with integer coordinates and an independent cell-occupancy check. No carton or tray was built. Mark the named rectangles on squared paper, keeping the identifying letters visible, so that the designer and shop manager can discuss the same objects. The drawing is a concrete explanation of the proposal rather than a photograph of a finished commercial package.

The decision is to keep the refill insert as a replenishment aid and retain the separate counter presentation. Remove the ready-to-display wording from the fictional offer. That is not a criticism of the insert’s purpose: an orderly refill can still be useful. The correction prevents a useful back-room design from being sold as a different service that the shop has not agreed to perform.

Make the transfer work visible in the offer

Write a short opening instruction for the shop assistant: identify the refill set, transfer it into the established display and retain any remaining stock in the designated back-room location. Use the retailer’s own approved product names and display reference in a real handoff. In this exercise those are fictional labels, but the structure should leave no doubt that unpacking and presentation are separate actions.

Do not invent a number of seconds for that work. The shop may have limited counter space, a different opening routine or a requirement to reconcile delivered stock before handling it. If the maker wishes to promise a faster setup, that claim needs relevant observed evidence. Here the honest offer simply acknowledges the transfer and allows the retailer to judge whether the refill arrangement is useful.

There are two legitimate commercial responses. The shop may accept the refill design because replenishment happens before opening and the established display already serves customers well. Alternatively, it may insist that staff should not need to transfer the sets. In that case the maker must reopen the presentation brief rather than quietly preserve the existing design and soften the wording in a footnote.

For the first response, provide separate illustrations of arrival and counter presentation. Give each a title that describes its purpose. Do not place the customer-facing illustration on the shipment drawing as though the package opens directly into that state. The relationship between the images should explain the work, not disguise it. A short arrow labeled transfer is more candid than a decorative transformation that implies no handling.

Release one accurate promise across the handoff

Update the fictional sales sheet, opening instruction and retailer briefing together. A corrected instruction will not resolve the misunderstanding if the sales headline still promises instant presentation. Conversely, removing the headline without telling the shop about the transfer leaves the operational surprise intact. Treat these as parts of one offer whose meaning needs to agree.

Keep the original proposal in the design discussion with a clear explanation of why its role changed. This helps the sales team describe the value that remains: a replenishment insert for the agreed assortment, accompanied by an explicit transfer step. They do not need to apologize for failing to deliver an unspecified universal package. They need to describe the actual arrangement accurately.

The final artifact is a paired arrival-and-display instruction with an honest offer sentence. It chooses the refill route for the fictional shop that accepts the transfer, while identifying the alternative brief for a shop that does not. Neither outcome purchases packaging or certifies a physical design. The useful production decision is where the maker’s work ends, what the retailer must do next and whether the commercial promise says so.

Make the reasoning concrete.

The shop accepts a transfer before opening, but the maker’s sales sheet promises instant presentation.

Choose the second offer for the shop that accepts the transfer; reopen the brief for any shop that does not.

Take the questions into your next brief.

Use these prompts in your own notes. Nothing is submitted from this page.

1. Promise

   What does ready to display lead the shop manager to expect?

2. Drawing

   Can you reconstruct both supplied arrangements and every intersection check?

3. Transfer

   What must the assistant do between receipt and presentation?

4. Alternative

   What changes if the retailer refuses that opening task?

5. Offer

   Do the sales sentence and opening instruction describe the same service?

Watch for the wrong conclusion.

• Using an arrival illustration as if it documented the finished counter presentation.
• Inventing setup-time savings without observed evidence.
• Changing the assortment silently to preserve a preferred drawing.

Sources & scope

The retail commission and dimensions are invented. Local arithmetic was executed; no physical package or handling process was tested.

• Optimal Rectangle Packing: New Results →Primary research paper · Supports: Containment and nonoverlap.