500 School Shirts, One 38-inch Pattern
A tailoring unit in Guwahati has a contract for 500 boys' school shirts in four sizes. The school's size chart is measured on the finished garment after washing: chest 38 in (96.5 cm) for the base size, body length 71 cm from high point shoulder to hem, and a tolerance of +/-1 cm. The chosen fabric is a 2/60s cotton poplin, 112 cm usable width, 115 g/m2, at Rs 180 per metre, with a declared residual shrinkage of 3% in warp and 1% in weft after the first 40 degree C wash. The unit owns only a base-size 38 in pattern and plans to grade the other three sizes by adding 5 cm to chest and 2 cm to length per size. Its marker consumes 1.32 m of fabric per shirt at 112 cm width, with 2% end loss. Cutting starts in ten days. The unit's manager proposes to simply add 3% to every pattern piece length instead of pre-shrinking the roll, because "the mill has already said 3%"
1. Calculate the fabric quantity, weight and cost to buy for the order, and check whether the 1.32 m consumption is plausible.
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Consumption. 500 shirts x 1.32 m = 660 m. Add 2% end loss: 660 x 1.02 = 673.2 m, so order 674 m (buy in whole rolls and check the roll length).
Weight. Mass per running metre = width x GSM = 1.12 m x 0.115 kg/m2 = 0.1288 kg/m. So 673.2 x 0.1288 = about 87 kg.
Cost. 674 x Rs 180 = Rs 1,21,320, roughly Rs 243 per shirt in fabric.
Is 1.32 m plausible? For a 112 cm wide poplin at 96.5 cm chest, two body panels need about 2 x 53 cm = 106 cm of the width, so the body occupies one width and 76–78 cm of length. Sleeves, yoke, collar, cuffs and pocket normally need another 45–50 cm of length if nested in the same width. Total 122–128 cm plus end loss lands close to 1.32 m, so the figure is plausible but tight - ask to see the marker, because a 3% shrinkage allowance (below) pushes it to about 1.36 m and that changes the order by roughly 20 m, or Rs 3,600.
Grading check. Adding 5 cm chest per size is roughly the standard 2 in step, but length steps for school shirts are usually 1.5–2 cm per size, not a flat 2 cm with no armhole, neck and shoulder adjustment. Approve a sewn sample in the smallest and largest size before cutting 500.
2. Should the 3% be handled by adding to the pattern or by pre-shrinking the fabric? Justify with numbers and say where a blanket addition goes wrong.
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Arithmetic. The 71 cm body length is measured after washing, so the cut length must be 71 / 0.97 = 73.2 cm, i.e. 2.2 cm added to the body. The same shrinkage applies to hems and seam allowances, so the cleanest method is to multiply the whole cut length by 1/0.97: 1.32 m becomes 1.36 m, a 4 cm increase and about Rs 7 more per shirt - Rs 3,600 on the order. That is trivially cheaper than one rejected lot of 500 shirts.
Where a blanket addition fails. (1) Width shrinkage is 1%, not 3%; adding 3% to the chest gives a shirt 2 cm too wide, outside the +/-1 cm tolerance, since 96.5 x 1.03 = 99.4 cm. (2) Pieces cut across the warp, such as a crosswise yoke or cuff, shrink in the other direction and can be cut short. (3) Fusible interlining shrinks differently from the shell; if the collar and placket interlining is not pre-shrunk, the front puckers after the first wash. (4) Placket length, button spacing and pocket placement must be scaled with the body, not left at base-size positions.
Recommendation. Do both: get the mill's written 3% guarantee, wash-test three shirts from the first bundle at the school's actual laundry conditions, and only then cut the balance. Rely on a pattern allowance for the 1% weft; use pre-shrinking or a compacted fabric if the wash test shows more than 3%.
3. After the first 50 shirts are washed, one bundle shrinks 5% instead of 3%. Diagnose and decide what to do with the remaining 450.
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Diagnosis, in order of likelihood. (1) The bundle came from a different roll or mill lot; residual shrinkage varies roll to roll even within one shade. (2) The wash was harsher than the test - 60 degree C or a longer cycle instead of 40 degree C, or tumble drying. (3) The roll was still under warp tension from the mill; the first wash released latent shrinkage rather than the declared 3%. (4) The fusible interlining on collar and placket pulled the fronts in, which reads as fabric shrinkage but is a construction fault. (5) Pressing stretched the panels and the wash relaxed them back.
Actions. Quarantine all uncut fabric. Identify the rolls used for the 50 shirts and compare with the remaining stock. Cut a 20 cm square from each remaining roll, mark 10 cm, wash at the school's conditions, and group rolls by measured shrinkage. Cut each group with its own allowance, not a single 3% for all. Check one washed shirt against the size chart to separate fabric shrinkage from interlining and pressing effects.
Disclosure. Tell the school what happened, show the per-roll test data, and agree the measurement method (washed, laid flat, measured at specified points). Silently adding 2% more to the remaining 450 risks a second failure and destroys the tolerance argument if the dispute escalates.