\$title AMPL Sample Problem (AMPL,SEQ=74) \$onText A sample problem to demonstrate the power of modeling systems. Fourer, R, Gay, D M, and Kernighan, B W, AMPL: A Mathematical Programming Language. AT\&T Bell Laboratories, Murray Hill, New Jersey, 1987. Keywords: linear programming, production planning, AMPL \$offText Set p 'products' / nuts, bolts, washers / r 'raw materials' / iron, nickel / tl 'extended t' / 1*5 / t(tl) 'periods' / 1*4 /; Parameter b(r) 'initial stock' / iron 35.8 , nickel 7.32 / d(r) 'storage cost' / iron .03, nickel .025 / f(r) 'residual value' / iron .02, nickel -.01 /; Scalar m 'maximum production' / 123 /; Table a(r,p) 'raw material inputs to produce a unit of product' nuts bolts washers iron .79 .83 .92 nickel .21 .17 .08; Table c(p,t) 'profit' 1 2 3 4 nuts 1.73 1.8 1.6 2.2 bolts 1.82 1.9 1.7 .95 washers 1.05 1.1 .95 1.33; Variable x(p,tl) 'production level' s(r,tl) 'storage at beginning of period' profit 'income minus cost'; Positive Variable x, s; Equation limit(t) 'capacity constraint' balance(r,tl) 'raw material balance' obj 'profit definition'; limit(t).. sum(p, x(p,t)) =l= m; balance(r,tl+1).. s(r,tl+1) =e= s(r,tl) - sum(p, a(r,p)*x(p,tl)); obj.. profit =e= sum((p,t), c(p,t)*x(p,t)) + sum((r,tl), (-d(r)\$t(tl) + f(r)\$tl.last)*s(r,tl)); s.up(r,tl)\$tl.first = b(r); Model ampl 'maximum revenue production problem' / all /; solve ampl maximizing profit using lp;