Question 21 of 27

Question 4.2 capital cost indexes (6 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. Power-law cost model P=aX^b for each machine class, with a, b and unit conventions as tabulated, and unit conversions 1 lb=0.4536 kg, 1 m³=1.308 yd³, 1 tonne=1.102 short ton.

Find. The 1997 capital cost of each machine.

Approach. Convert each machine’s given size into the formula’s OWN native unit first, then apply P=aX^b directly.

1. 4.2.1 — drill. $$X = \dfrac{55{,}000\text{ kg}}{0.4536\text{ kg/lb}} = 121{,}252\text{ lb}$$ $$P = 4{,}000 \times 121{,}252^{0.67}$$ $$\boxed{P \approx \$10.19\text{ million}}$$
2. 4.2.2 — shovel. $$X = 53\text{ m}^3 \times 1.308\text{ yd}^3/\text{m}^3 = 69.32\text{ yd}^3$$ $$P = 5{,}350{,}000 \times 69.32^{0.74}$$ $$\boxed{P \approx \$123.20\text{ million}}$$
3. 4.2.3 — truck. $$X = 300\text{ tonne} \times 1.102\text{ ton/tonne} = 330.6\text{ short ton}$$ $$P = 20{,}000 \times 330.6^{0.90}$$ $$\boxed{P \approx \$3.70\text{ million}}$$