Applied Mathematical Programming by Stephen P. Bradley

By Stephen P. Bradley

Booklet by means of Bradley, Stephen P., Hax, Arnoldo C., Magnanti, Thomas L.

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Of hours Mining final products) per 1 ton of Mine Method ($) final products A 1 250 50 2 320 62 3 260 63 B 4 210 55 5 350 60 Quality 65% 80% 76% 76% 78% Production Production capacity Distribution (tons of Product Product Product crude material) I II III 300 20% 30% 50% 280 25% 35% 40% 400 15% 45% 40% 250 7% 24% 69% 500 35% 40% 25% Note that the mining costs are per 1 ton of final products, and not per 1 ton of crude mineral. The production capacity of each mining method is in terms of crude material.

Indeed, the substitution is merely the familiar variable-elimination technique from high-school algebra, known more formally as Gauss–Jordan elimination. 1 In summary, the basic step for generating a canonical form with an improved value for the objective function is described as: Improvement Criterion. Suppose that, in a maximization problem, some nonbasic variable has a positive coefficient in the objective function of a canonical form. If that variable has a positive coefficient in some constraint, then a new basic feasible solution may be obtained by pivoting.

The company diverts a portion of the river water, adds the pollutants, namely, phenol and nitrogen, to it, and sends the water back to the river. The company has four possible ways to treat the water it uses before returning it to the river. The characteristics of each treatment are given in the following table: (lbs. of pollutant)/MG after treatment Treatment 1 2 3 4 Phenol Nitrogen P1 N1 P2 N2 P3 N3 P4 N4 Cost/MG c1 c2 c3 c4 Assume: (i) that the river is initially free of pollutants; (ii) that addition of pollutants does not affect the amount of water flow; and (iii) that the company has to process at least K (MG/day) of river water.

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