Question 6 of 6: Estimating — completing an R.S. Means masonry line

Question 6: Estimating — completing an R.S. Means masonry line (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. One R.S. Means unit-price line and its related crew table, both partly blank, together with the quantity to be built and the crew the contractor intends to use.

Find. The completed crew table and unit-price line — daily output, bare labour and total unit costs, and the same figures including overhead and profit — and then the total cost and the duration of the 6,000 S.F. job when it is built with five bricklayers and three helpers.

Approach. Price the crew from its composition and wage rates, recover the missing daily output from the labour-hour column, complete both tables, and then re-time and re-price the job on the crew actually deployed.

1. Read the line description correctly before pricing anything. The parenthesis in "Economy, 4" × 4" × 8" (4.50/S.F.)" is a coursing density: 4.50 bricks are required per square foot of wall face. It is not a unit price. Every column in the Means line — labour hours, material, labour, total — is already expressed per square foot, and the take-off is given in square feet, so the density is used only to order material: $6{,}000 \times 4.50 = 27{,}000$ bricks. Pricing the brick count against the per-square-foot rates instead would multiply the estimate by four and a half, and it is the dominant wrong answer on this style of question.
2. Price crew D-8. A Means crew day is eight hours, so the crew's own line confirms itself: five workers times eight hours is the printed 40 total hours. The bare daily cost is the sum of the two trades, $$C_{\text{bare, daily}} = 3(8)(35.25) + 2(8)(26.90) = 846.00 + 430.40 = \$1{,}276.40$$ and dividing by the 40 labour-hours gives the figure the Means "Cost Per Labor-hour" column asks for: $$c_{\text{bare}} = \frac{1{,}276.40}{40} = \$31.91\ \text{per labour-hour}$$ Applying the stated 60 % overhead and profit to labour, $$c_{\text{O\&P}} = 31.91 \times 1.60 = \$51.06\ \text{per labour-hour}, \qquad C_{\text{O\&P, daily}} = \$2{,}042.24$$
3. Recover the missing daily output. The blank Daily Output cell is not missing information — it is implied exactly by the labour-hour column, because the two describe the same productivity from opposite ends: $$Q_{\text{day}} = \frac{\text{crew labour-hours per day}}{\text{labour-hours per unit}} = \frac{40}{0.129} = \boxed{310\ \text{S.F. per day}}$$ The self-check is that the job duration computed from the output must equal the duration computed from the labour hours, and it does: $6{,}000/310.08 = 774/40 = 19.35$ crew-days.
4. Complete the unit-price line. Bare labour per square foot is the labour content times the bare crew rate, $$\text{Labor} = 0.129 \times 31.91 = \$4.12\ \text{/ S.F.}$$ Crew D-8 carries no equipment, so that column is nil, and the bare total is $$\text{Bare total} = 3.54 + 4.12 + 0 = \$7.66\ \text{/ S.F.}$$ Applying the 60 % to the labour component only, as the question directs, gives the "Total incl. O&P" figure: $$\text{Total incl. O\&P} = 3.54 + 4.12(1.60) = 3.54 + 6.59 = \boxed{\$10.13\ \text{/ S.F.}}$$

5. Re-time the job on the crew actually used. The labour content of the work does not change with crew size; only the rate at which it is consumed does. The job contains $$LH = 6{,}000 \times 0.129 = 774\ \text{labour-hours}$$ and five bricklayers with three helpers deliver $8 \times 8 = 64$ labour-hours per day, so $$t = \frac{774}{64} = \boxed{12.1\ \text{working days}}$$ which is 13 working days on site, or about two and a half working weeks. The same answer follows from the daily output, which scales with the crew: $310.08 \times (64/40) = 496.1$ S.F. per day and $6{,}000/496.1 = 12.1$ days. That agreement between the two routes is the productivity self-check, and it holds because the deployed crew keeps very nearly the Means proportion of bricklayers to helpers.
6. Price the job on the crew actually used. The deployed crew is 62.5 % bricklayers against the Means crew's 60 %, so its blended wage is slightly higher: $$c'_{\text{bare}} = \frac{5(8)(35.25)+3(8)(26.90)}{64} = \frac{2{,}055.60}{64} = \$32.12\ \text{per labour-hour}$$ Material is unaffected by how the wall is manned, so the estimate assembles as $$\text{Material} = 6{,}000 \times 3.54 = \$21{,}240.00$$ $$\text{Labour, bare} = 774 \times 32.11875 = \$24{,}859.91 \quad\Longrightarrow\quad \text{Labour incl. O\&P} = 24{,}859.91 \times 1.60 = \$39{,}775.86$$ $$\text{Total} = 21{,}240.00 + 39{,}775.86 = \boxed{\$61{,}015.86 \approx \$61{,}000}$$ that is $10.17 per square foot. Against the $10.13 per square foot of the completed Means line the difference is 0.4 %, entirely explained by the richer bricklayer proportion — a useful cross-check that neither table has been mis-priced.