Chapter 12 — Exercises

Work these with a calculator and a pencil, not in your head. Items marked † have worked solutions in the answers appendix; everything else is yours to defend. Where an exercise asks for a judgment, the arithmetic is the easy half — the sentence explaining why is the graded part.

Unless an exercise says otherwise, use Bellwether's dinner-entrée week from the chapter:

(330 units · $8,739.00 entrée sales · $2,447.98 ideal food cost · 28.0% blended · weighted CM $19.06)

Recall and definitions

12.1 Define contribution margin in one sentence, and state the arithmetic that produces it.

12.2 What are the two axes of the menu-engineering matrix, and what does each one measure?

12.3 Name the four quadrants and give the one-word default action for each.

12.4 † A menu category has eight items. What is the expected mix share per item, and what is the popularity threshold under the conventional 70% rule? Show both figures.

12.5 Why does menu mix count units rather than sales dollars? Give the specific distortion that using dollars introduces.

12.6 Explain the difference between the simple average of a menu's contribution margins and the weighted average. Which one is the matrix's horizontal line, and why?

12.7 What does a popularity index of 0.68 tell you about an item, in plain language?

12.8 Whose framework is the star/plowhorse/puzzle/dog matrix usually attributed to, and roughly when? What is the honest status of the 70% popularity threshold — a research finding or a convention?

Applied reasoning

12.9 † An operator tells you their best item is the one with the lowest food cost percentage. Write the three-sentence reply you would give, using a numerical example of your own construction.

12.10 Bellwether's five contribution margins fit inside a band of $5.01. Explain what that flatness implies about how much menu engineering can achieve at this restaurant through mix shifts, and where the leverage sits instead.

12.11 Why is it a mistake to put appetizers and entrées in the same matrix? Answer with reference to both axes, not just one.

12.12 An item's plate cost falls by $1.00 and its quadrant does not change. Give the mechanical reason, and state the rule of thumb from §12.5 that predicts it.

12.13 † Bellwether cuts the ember trout. Using the chapter's Round 2 figures, explain why the Bellwether burger's position gets worse even though nothing about the burger changed.

12.14 The chapter says the matrix is "a ranking wearing the costume of a standard." Explain that sentence to someone who has just been shown a POS report with quadrant labels on it.

12.15 A restaurant runs a twenty-item menu. Compute its popularity threshold under the 70% rule, and explain why items fall below it far more often than on Bellwether's five-item menu.

Cost this / compute this

12.16 † Compute the menu mix percentage for all five Bellwether entrées to one decimal place, and verify that they sum to 100.0%. Then compute each item's popularity index and verify that the five indices sum to 5.00.

12.17 Compute total contribution margin two different ways: (a) as the sum of units × CM, and (b) as entrée sales minus ideal food cost. Show that they agree, and say why an operator should always run both.

12.18 A dish sells for $26.00 with a plate cost of $7.15. Compute its food cost percentage and its contribution margin. It sells 38 units in a nine-item category totaling 295 units — compute its menu mix percentage, the category's popularity threshold under the 70% rule, and the dish's popularity index.

12.19 † Bellwether's March poultry renewal takes air-chilled chicken from $3.20/lb to $3.85/lb. Rebuild the Hearth Chicken cost card (half of a 3.5 lb bird; other components $2.75; 2% waste allowance on components) and compute the new plate cost, food cost percentage, and contribution margin at the unchanged $29.00 price. What is the annual cost of doing nothing?

12.20 Using the answer to 12.19, recompute the menu's weighted average contribution margin with all other items and all unit counts unchanged. Does the Hearth Chicken remain above the line?

12.21 † The squash and grains sits $0.99 above the weighted average CM with an 18.8% mix. Using the rule that a cost move closes the gap at (1 − mix share) per dollar, compute the plate-cost increase that would flip it from Star to Plowhorse. Then verify your answer by recomputing both the item's CM and the menu's weighted average.

12.22 A four-week product-mix report shows 1,320 entrées. Recompute all five mix shares assuming each item sold exactly four times its weekly figure, and confirm that the quadrant placements do not change. What did change, and why does it matter?

Price this / engineer this menu

12.23 † You are considering taking the Bellwether burger from $21.00 to $22.50. Compute the new contribution margin, the break-even unit volume, and the percentage of burger volume you could lose before the change costs you money. State whether you would do it and why.

12.24 The pork chop drops to 41 units a week; nothing else changes. Recompute total units, total contribution margin, the weighted average CM, and all five mix shares. Then place all five items and state which one changed quadrant and which one changed for a reason that has nothing to do with it.

12.25 Design a $4.50 side dish intended to attach to the Bellwether burger. Specify a plate cost, compute the contribution margin, assume an attachment rate you can defend, and compute the annual value. Then state the one operational reason your attachment rate might be optimistic.

12.26 † Here is a five-item lunch menu at a different restaurant (constructed teaching example). Build the complete matrix: mix percentages, weighted average CM, the 70% threshold, and a quadrant for every item. Show every step.

(600 units in total. Your mix shares should sum to exactly 100.0% at one decimal place; if they do not, find the arithmetic error before you go any further.)

12.27 Using your answer to 12.26, propose two — and only two — re-engineering actions for the next period. For each, state the expected dollar effect and how you would know in four weeks whether it worked.

12.28 A consultant recommends cutting the two lowest-margin items from the menu in 12.26. Compute the resulting weighted average CM and threshold on the remaining three items, assuming no substitution, and identify the new bottom item. Write the two-sentence objection you would raise in the meeting.

Read this report and find the problem

12.29 † A product-mix report for a twelve-item dinner menu shows one item — "OPEN ENTREE" — at 7% of units with a plate cost field left blank. Explain what is almost certainly happening, what it does to the other eleven items' mix shares, and the two things you would do before running the matrix.

12.30 A four-week matrix shows the same dish appearing twice, once at 6.1% mix and once at 5.4%, under names that differ by one word. Explain the cause, the effect on both axes, and the fix.

12.31 An operator's matrix places every single item above the popularity threshold. Give two different explanations — one about the menu, one about the analysis — and say how you would tell them apart.

12.32 A restaurant's food cost report improves from 31% to 28% over two quarters while operating profit falls. Using this chapter and Chapter 1, name three mechanisms that could produce that pattern and describe the single report you would pull first.

Write this

12.33 Write the one-page memo to a chef explaining why the highest-food-cost item on the menu is not going to be cut this quarter. Use real arithmetic, name the risk you are accepting, and state the date and the trigger at which you will revisit the decision.

12.34 † Write the pre-shift script — 90 seconds, spoken — that a manager would use to move a Puzzle. It must describe the dish, give the server one specific sentence to say at the table, and state what will be measured.

12.35 Write the standing agenda for a 45-minute monthly menu-engineering meeting, including who attends, what must be true before it starts, and the one item that ends the meeting early if it fails.

Judgment and ethics

12.36 The matrix says to cut the only vegetarian entrée on your menu. Work through the decision, naming at least four considerations the matrix cannot see. State what you would do and what evidence would change your mind.

12.37 † Your kitchen proposes fixing a Plowhorse by reducing the protein portion from six ounces to five, without changing the price or the menu description. Evaluate this as (a) arithmetic, (b) a guest-experience decision, and (c) a question of honesty. Where, if anywhere, is the line?

12.38 A dish is a genuine Dog by both axes and has been for three periods. It is also the only thing on the menu that a regular guest of four years orders. What do you do, and what does your answer say about how you weight measurable and unmeasurable value?

12.39 Your POS vendor's built-in menu-engineering report labels items using a threshold it does not disclose. Describe the professional obligation you have before presenting those labels to your chef, your partner, or anyone whose job might be affected by them.

Business Plan extensions

12.40 † Build Bellwether's menu-engineering appendix as a one-page document a plan reader could evaluate: the projected mix, the CM ranking, the quadrant placement, and a clearly labeled statement of which numbers are arithmetic and which are forecast.

12.41 Bellwether's plan targets 30% food cost; the projected entrée mix produces 28.0% ideal. Write the two-sentence note that belongs in the plan explaining why the two points are not being spent, and quantify what those two points would be worth on the plan's food sales if they were real.

12.42 Write the three commitments Bellwether should put in writing about how it will run this analysis in year one — cadence, ownership, and the specific date at which the ember trout decision gets made rather than deferred. Then state what evidence would have to arrive for each commitment to be worth keeping.