Measurement Tolerance and Waste Allowance in Floor Tiling
A rectangular dance floor measures 9.6 m by 7.2 m, each dimension recorded to the nearest 0.1 m. It is to be covered with 0.8 m square panels sold in bundles of 12. The installer allows 8% waste. An assistant rounds both dimensions to the nearest metre first, obtains 10 m × 7 m = 70 m², adds 8%, and orders 7 bundles. The installer uses the measured dimensions and also checks the effect of measurement tolerance. Each bundle covers 7.68 m². The supplier charges a 15% restocking fee for unused full bundles, but a second delivery takes 10 days and would delay the job. The floor may be laid in line with the walls or diagonally; diagonal laying raises waste to 14%.
1. Check the assistant's bundle count and the installer's count. Include the measurement tolerance and state the minimum safe number of bundles for straight laying.
Read the worked answer
Assistant: 70 × 1.08 = 75.6 m², and 75.6 ÷ 7.68 = 9.84, so 10 bundles are needed, not 7. Seven bundles cover only 7 × 7.68 = 53.76 m², which is far too little.
Installer: 9.6 × 7.2 = 69.12 m²; 69.12 × 1.08 = 74.6496 m²; 74.6496 ÷ 7.68 = 9.72, so 10 bundles.
Tolerance: the dimensions lie in [9.55, 9.65] and [7.15, 7.25] m. Worst-case area is 9.65 × 7.25 = 69.9625 m². With 8% waste this is 69.9625 × 1.08 = 75.5595 m², and 75.5595 ÷ 7.68 = 9.838, still 10 bundles. Ten bundles cover 76.8 m², leaving 1.24 m² above the worst case. Minimum safe order: 10 bundles.
2. For diagonal laying, how many bundles are needed under worst-case dimensions? Let P be the bundle price. Compare ordering 11 immediately with ordering 10 and possibly needing a second delivery.
Read the worked answer
Worst-case diagonal need is 69.9625 × 1.14 = 79.75725 m². Dividing by 7.68 gives 10.386, so 11 bundles are needed.
Ordering 11 immediately guarantees no delay. If only 10 are used, one full bundle is returned for a 15% restocking fee, so the net cost is 11P − 0.85P = 10.15P. Ordering 10 risks a 10-day delay if 11 are needed, with cost 11P plus the delay. Thus ordering 11 is justified when the cost of a 10-day delay exceeds 0.15P, or when the probability of needing the extra bundle is high enough. Otherwise 10 plus a possible second order may be acceptable. The decision is a trade-off between waste cost and delay risk, not a pure area calculation.