Pencil-Case Production for Open Day
JHS 3 at a school in Cape Coast must produce 30 pencil cases for an open day. The class has GHS 180. Local wax-print fabric costs GHS 12 per metre and is 1.2 m wide. Each pencil case needs 0.25 m of outer fabric and 0.20 m of lining. Lining costs GHS 6 per metre. Zippers cost GHS 3 each. Thread costs GHS 8 per spool, and one spool is enough for 20 cases. The class has six sewing machines, but two are broken. There are 24 students and three weeks, with two double periods (80 minutes each) per week. A parent has donated 4 m of lining. The teacher wants every student to take part and the cases to be sold at GHS 10 each. The open day is fixed.
1. Calculate the total cost of making 30 cases using the donated lining. State whether the GHS 180 budget is sufficient.
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Outer fabric: 30 × 0.25 m = 7.5 m. Cost = 7.5 × GHS 12 = GHS 90. Lining: 30 × 0.20 m = 6 m needed. Parent donated 4 m, so buy 2 m. Cost = 2 × GHS 6 = GHS 12. Zippers: 30 × GHS 3 = GHS 90. Thread: one spool covers 20 cases, so 30 cases need 2 spools. Cost = 2 × GHS 8 = GHS 16. Total = 90 + 12 + 90 + 16 = GHS 208. The budget is GHS 180, so there is a shortfall of GHS 28. Expected sales revenue is 30 × GHS 10 = GHS 300, so the project is profitable in principle, but the class cannot buy all materials with the cash available unless it obtains extra funds or changes the plan.
2. Propose two realistic ways to bring the project within budget without cancelling the open-day order, and evaluate one trade-off.
Read the worked answer
Option 1: make 24 cases, one per student. Outer: 24 × 0.25 = 6 m = GHS 72. Lining: 24 × 0.20 = 4.8 m; use 4 m donated, buy 0.8 m = GHS 4.80. Zippers: 24 × 3 = GHS 72. Thread: still 2 spools = GHS 16 (because 24 > 20). Total = GHS 164.80, within budget. Revenue at GHS 10 = GHS 240. Trade-off: the open-day order is for 30 cases, so the class must explain the shortfall or ask six students to make a second case using offcuts, which may not be possible. Option 2: request GHS 30 from the PTA or negotiate a lower zipper price (for example GHS 2.50 each saves GHS 15). A combination - 28 cases plus a small top-up - may better protect the order. The teacher should not silently reduce quality; the trade-off is quantity and promise-keeping versus budget discipline.
3. Plan the use of the four working machines over the three weeks so that all 24 students participate and 30 cases are finished.
Read the worked answer
With four working machines and 24 students, divide the class into four teams of six, each team assigned a machine and a rotating stage. Week 1: cut outer fabric and lining using templates; one team measures, one cuts, two mark and pin. Week 2: attach zippers and sew outer panels; teams rotate so every student sews at least one seam. Week 3: attach lining, turn and finish, quality check, label and price. Each 80-minute session has a 10-minute demonstration, 55 minutes production and 15 minutes clean-up and record-keeping. Assign six volunteers (or a second case to six students) to reach 30 cases; use the last session for finishing and inspection. Check machine safety, needle guards and supervised plug use; two broken machines are not used.