Fabric Budget and Deadline for a Shirt Order
Your self-help group has won an order for 60 school shirts. Each shirt needs 1.75 m of 90 cm-wide fabric. The supplier sells fabric only in full metres and quotes ₹85 per metre. The group's cutting table records 9% wastage because the stripes must be matched. The group has ₹8,500 set aside for fabric. Four women will sew, and each shirt takes 40 minutes of sewing. Because of household work, the four can together give only 3 hours per day to sewing. The order must be delivered in 7 working days. Cutting takes 1 hour per 10 shirts and must be completed before stitching starts; the group plans to use the first day for cutting. The customer will pay only after delivery, so the group cannot use the order money to buy fabric.
1. Calculate the fabric needed, the cost, and whether the ₹8,500 budget is enough. Show the rounding decision for full metres and the 9% wastage.
Read the worked answer
Fabric per shirt = 1.75 m. For 60 shirts, base fabric = 60 × 1.75 = 105 m. Wastage = 9% of 105 = 9.45 m. Total = 114.45 m. Because the supplier sells only full metres, the group must buy 115 m, not 114 m; buying 114 m would leave the order 0.45 m short if wastage is exactly 9%. Cost = 115 × ₹85 = ₹9,775. Budget = ₹8,500. Shortfall = ₹9,775 − ₹8,500 = ₹1,275. So the budget is not enough. Rounding up matters: even 114 m would cost ₹9,690, still over budget. The group cannot place the fabric order on the current budget.
2. The group leader says, 'If we reduce wastage to zero, we can fit the budget.' Test this claim with numbers and state what the group must actually do.
Read the worked answer
The leader's claim is false. With zero wastage, the group still needs 105 m, which costs 105 × ₹85 = ₹8,925. That is ₹425 more than ₹8,500. Zero wastage is also unrealistic when stripes must be matched, so the real need is higher. The group cannot solve the problem by cutting wastage alone. It must either obtain at least ₹1,275 more (or ₹425 in the impossible zero-wastage case), find fabric at a lower rate, or ask the customer for an advance. The maximum fabric affordable at ₹85 is ₹8,500 ÷ ₹85 = 100 m, which is 5 m less than the base requirement before any wastage. A lower price would help: at ₹80/m, 115 m costs ₹9,200, still short; the group should compare offers rather than assume a small discount is enough.
3. Ignoring the fabric problem for a moment, decide whether the group can finish stitching by the 7-day deadline if cutting takes all of day 1. Show the daily sewing capacity and the number of stitching days needed.
Read the worked answer
Sewing labour required = 60 shirts × 40 minutes = 2,400 minutes = 40 hours. Daily sewing capacity = 4 women × 3 hours = 12 woman-hours per day. Days needed = 40 ÷ 12 = 3.33 days, so 4 sewing days in practice. If day 1 is used entirely for cutting, stitching starts on day 2. Four sewing days from day 2 means finishing on day 5. The 7-day deadline is therefore feasible with two days to spare, provided the fabric arrives before day 1 and the women are available on all four sewing days. The binding constraint is money, not time. The group should not celebrate the deadline until the fabric is secured.