24-MMP-A4 Mine Valuation and Mineral Resource Estimation · December 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Mining and Mineral Processing Engineering, 09-Mmp-A4 Mine Valuation and Mineral Resource Estimation, 2014-Dec. 3 hours duration; one handwritten 8.5×11 in reference sheet permitted (not an open-book exam); only approved Sharp or Casio calculators allowed. Question 1 is compulsory (40 marks, parts 1.1–1.7); candidates then select FOUR of the six optional Questions 2–7 (15 marks each) to complete the paper.
Reference texts: Isaaks & Srivastava, An Introduction to Applied Geostatistics (variogram modelling, kriging estimators, volume–variance relations); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (mine valuation, NPV and cut-off grade methodology, mineable reserves); Gentry & O'Neil, Mine Investment Analysis (Canadian mining taxation, smelter/refining contract terms, net smelter return); SME Mining Engineering Handbook, 3rd ed. (mineral exploration/evaluation stages, ore reserve classification); CIM Best Practice Guidelines and NI 43-101 (Canadian Securities Administrators).
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.
The value −0.1250 is μ, the Lagrange multiplier introduced into the kriging system specifically to enforce the unbiasedness constraint Σwi = 1 while minimizing estimation variance. It is a mathematical artifact of the constrained-optimization solution, not a grade or a weight itself, and it carries no direct physical/grade meaning on its own — but it is not discarded, because it enters the minimized ordinary-kriging variance formula directly: $$\sigma^2_{OK}=C(B,B)-\sum_i w_i C_{i,B}-\mu$$ so μ quantifies the marginal "cost," in variance terms, of imposing the unbiasedness constraint on the estimate. A negative μ (as here) is the typical sign for ordinary kriging and increases the reported estimation variance above what an (unconstrained, and therefore potentially biased) simple-kriging solution would give.
