Tiling the JHS Computer Room
A headteacher plans to tile the floor of a rectangular JHS computer room measuring 7.2 m by 5.4 m. A fixed cabinet occupies a 1.0 m by 0.4 m area that will not be tiled. The chosen tiles are square, 30 cm by 30 cm. Supplier A sells only full boxes of 12 tiles at GHS 48 per box. Supplier B sells individual tiles at GHS 4.50 each and charges a flat delivery fee of GHS 25, but will refund unused whole tiles at the purchase price. The school expects about 5% of tiles to be cut or broken during installation. Labour will cost GHS 600 whichever supplier is used. The headteacher wants to avoid a second order because the room must be ready for an ICT practical in two weeks. Compare the two suppliers and advise the headteacher, showing all working.
1. Calculate the number of tiles required after allowing for the cabinet and the 5% wastage, then compute the total cost (tiles plus labour) for each supplier.
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Step 1: area to tile. Room area = 7.2 × 5.4 = 38.88 m². Cabinet = 1.0 × 0.4 = 0.40 m². Tiled area = 38.48 m².
Step 2: tile count. Each tile = 0.30 × 0.30 = 0.09 m². Exact tiles = 38.48 ÷ 0.09 = 427.56, so 428 whole tiles before waste. Allowing 5% waste: 428 × 1.05 = 449.4, so plan for 450 tiles.
Step 3: Supplier A. Boxes needed = 450 ÷ 12 = 37.5, so 38 full boxes = 456 tiles. Tile cost = 38 × GHS 48 = GHS 1,824. Labour = GHS 600. Total = GHS 2,424.
Step 4: Supplier B. 450 tiles × GHS 4.50 = GHS 2,025. Add delivery GHS 25 and labour GHS 600. Total = GHS 2,650.
Advice: Supplier A is cheaper by GHS 226 (2,650 − 2,424), and it gives 6 spare tiles as a buffer. Supplier B is only worth considering if the school expects to return many whole tiles unused; that is unlikely with a 5% waste allowance.
2. The headteacher says, 'Supplier B is safer because we can return unused tiles.' Evaluate this claim using the figures and one practical risk.
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Supplier B's return policy applies only to unused whole tiles. Cut, broken or fixed tiles cannot be returned, so the 5% waste is a sunk cost under either supplier. On the expected figures, B still costs GHS 226 more after the refund policy is considered. The return policy mainly protects against over-ordering, not against breakage. A practical risk is that the 5% estimate is too low: if breakage is 10%, A's 456 tiles (6 spare) may be insufficient and a second order may miss the two-week deadline, while B could buy extra tiles immediately but at a higher unit price and with a delivery delay. The headteacher should check the tiler's breakage estimate for this tile type and confirm that Supplier A can deliver all 38 boxes at once. If not, B's flexibility may justify part of the extra cost.
3. State two assumptions in your comparison and explain how one could change the decision.
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Two assumptions: (1) the 5% waste rate includes both cutting and breakage; (2) all 456 tiles from Supplier A are usable and no box is short. A third assumption is that labour is unchanged. If the tiler can reuse offcuts from the 1.0 m × 0.4 m cabinet area, waste may be lower, which helps B's refund policy but does not close the GHS 226 gap unless a large number of whole tiles are returned. If the school values speed and flexibility more than GHS 226, the decision could change. Otherwise A remains the lower-cost, lower-risk choice for a fixed deadline.