Meeting a 40-desk order with short timber and a broken mortiser
A school workshop must produce 40 student desks in three weeks. Stock: 20 sheets of 18 mm plywood, each 1,220 mm × 2,440 mm, and 80 pieces of 50 mm × 50 mm cypress, each 3.6 m long. Each desk needs a top 1,200 mm × 450 mm and a frame: 4 legs 720 mm, 2 long rails 1,080 mm, 2 short rails 380 mm and 1 stretcher 1,000 mm. Allow 3 mm saw kerf and 10% wastage on timber; plywood cutting loses about 10% to trimming. The mortiser is broken; only a circular saw, drill, chisels and clamps are available. Two technicians work 6 hours a day, 5 days a week; each desk takes about 2.5 labour hours. Plywood costs KSh 1,800 per sheet and cypress KSh 650 per piece. The head teacher wants all 40 desks and a clear statement of any shortfall.
1. Calculate whether the available plywood and cypress are sufficient for 40 desks, showing the effect of wastage and kerf.
Read the worked answer
Plywood: top area = 1.2 × 0.45 = 0.54 m². Sheet area = 1.22 × 2.44 = 2.9768 m². Allowing 10% cutting loss, usable area = 2.679 m² per sheet. Tops per sheet = 2.679 ÷ 0.54 = 4.96, so only 4 complete tops can be cut per sheet after trimming. Twenty sheets yield 80 tops, enough for 40 desks. In fact 10 sheets yield 40 tops, leaving 10 sheets spare. Plywood is therefore not the constraint.
Cypress: frame length per desk = (4 × 0.72) + (2 × 1.08) + (2 × 0.38) + 1.00 = 2.88 + 2.16 + 0.76 + 1.00 = 6.80 m. Add 10% wastage and kerf allowance: 6.80 × 1.10 = 7.48 m per desk. Total timber available = 80 × 3.6 = 288 m. Desks possible = 288 ÷ 7.48 = 38.5, so only 38 complete desks can be made. The shortfall is 2 desks, requiring 2 × 7.48 = 14.96 m, or 5 additional cypress pieces (18 m), costing 5 × 650 = KSh 3,250.
Labour: 40 × 2.5 = 100 hours needed. Available = 2 technicians × 6 h × 5 days × 3 weeks = 180 hours, so labour is sufficient if organised well.
2. Recommend a jointing method and construction sequence given that the mortiser is broken. Justify the choice for school desks.
Read the worked answer
Use hand-cut mortise-and-tenon joints for the leg-to-rail connections, cut with a drill and chisel using a simple plywood template, and a halving joint for the stretcher. Glue all joints and add a glued corner block at each leg-rail junction. Although the mortiser is broken, a template allows one operator to mark and cut repeatable mortises while the other prepares tenons on the circular saw. This preserves the racking strength that school desks need; butt joints fixed only with nails or screws will loosen under sideways loading.
If time proves tight, a acceptable fallback is three 10 mm dowels per joint with polyurethane glue, drilled through a jig. Dowels are faster than hand-cut mortises but weaker in tension; they should be used only with corner blocks and a stretcher. Do not omit the stretcher to save timber: the stretcher is what prevents the legs from splaying, and removing it would create a repair problem later.
Sequence: week 1, cut all plywood tops, timber components and jigs; week 2, cut joints and dry-fit in batches of ten; week 3, glue and assemble, sand, then apply two coats of varnish. Batch production reduces setting-up time and allows the second technician to finish earlier batches while joints cure.
3. Prepare a short production schedule and state what should be bought first within a KSh 15,000 contingency.
Read the worked answer
Buy the 5 extra cypress pieces first (KSh 3,250), because without them the order cannot be completed. Then buy glue, dowels or chisel consumables and varnish from the remaining contingency. The 10 spare plywood sheets provide material for jigs and corner blocks; they should not be counted as desks.
Schedule:
- Days 1–2: set up jigs, cut plywood tops in batches, machine all cypress to size, allowing for 7.48 m per desk.
- Days 3–7: cut mortises and tenons; dry-assemble 10 desks and check for squareness.
- Days 8–10: glue and assemble the remaining desks; fit stretchers and corner blocks.
- Days 11–13: sand all surfaces and apply first varnish coat.
- Days 14–15: light sand and apply second coat; inspect and stack.
The critical path is joint cutting, not assembly or finishing. With 180 labour hours available and 100 hours of direct work, there is slack for rework, but only if the extra timber is bought immediately. If the 5 pieces cannot be obtained, the workshop should tell the head teacher now that 38 desks will be ready and negotiate a revised delivery date rather than promise 40 and fail.