A description of the blast furnace production process is presented and the thermochemical metallurigcal process is expressed as a set of constraints of a linear programming problem. The solution indicates a minimum cost selection of input materials in a production planning context. The material presented here is dedicated to those who are engaged in the mathematical modelling of chemical and other complex processes for purposes of management control. It is also hoped that by adding the paper to the literature of detailed examples, a case study, often desired for classroom instruction, will be provided to educators.