\$title Blending Problem I (BLEND,SEQ=2) \$onText A company wishes to produce a lead-zinc-tin alloy at minimal cost. The problem is to blend a new alloy from other purchased alloys. Dantzig, G B, Chapter 3.4. In Linear Programming and Extensions. Princeton University Press, Princeton, New Jersey, 1963. Keywords: linear programming, blending problem, manufacturing, alloy blending \$offText Set alloy 'products on the market' / a*i / elem 'required elements' / lead, zinc, tin /; Table compdat(*,alloy) 'composition data (pct and price)' a b c d e f g h i lead 10 10 40 60 30 30 30 50 20 zinc 10 30 50 30 30 40 20 40 30 tin 80 60 10 10 40 30 50 10 50 price 4.1 4.3 5.8 6.0 7.6 7.5 7.3 6.9 7.3; Parameter rb(elem) 'required blend' / lead 30, zinc 30, tin 40 / ce(alloy) 'composition error (pct-100)'; ce(alloy) = sum(elem, compdat(elem,alloy)) - 100; display ce; Variable v(alloy) 'purchase of alloy (pounds)' phi 'total cost'; Positive Variable v; Equation pc(elem) 'purchase constraint' mb 'material balance' ac 'accounting: total cost'; pc(elem).. sum(alloy, compdat(elem,alloy)*v(alloy)) =e= rb(elem); mb.. sum(alloy, v(alloy)) =e= 1; ac.. phi =e= sum(alloy, compdat("price",alloy)*v(alloy)); Model b1 'problem without mb' / pc, ac / b2 'problem with mb' / pc, mb, ac /; Parameter report(alloy,*) 'comparison of model 1 and 2'; solve b1 minimizing phi using lp; report(alloy,"blend-1") = v.l(alloy); solve b2 minimizing phi using lp; report(alloy,"blend-2") = v.l(alloy); display report;