$title transportation model with taxes: linear complementarity set i supply nodes / omaha, madison /; set j demand nodes / portland, topeka, atlanta /; *quantities supplied and demanded parameter supply(i) / omaha 20, madison 30 /; parameter demand(j) / portland 15, topeka 10, atlanta 20 /; * tax applied at the supply node parameter tax(i) / omaha 0.10, madison 0.065 /; * cost of shipping from supply nodes to demand nodes table cost(i,j) portland topeka atlanta omaha 10 2 15 madison 15 5 10; positive variable x(i,j) amount shipped from i to j; positive variable m_supply(i) marginal supply price at supply node i; positive variable m_demand(j) marginal demand price at demand node j; equation supply_con(i), demand_con(j) supply and demand satisfaction; equation deliver_con(i,j) keep prices consistent; * flow out of i does not exceed supply supply_con(i).. supply(i) =g= sum(j, x(i,j)); * flow into i meets demand demand_con(j).. sum(i, x(i,j)) =g= demand(j); * demand price at j at least equal to supply price at i + tax + transportation deliver_con(i,j).. m_supply(i)*(1+tax(i)) + cost(i,j) =g= m_demand(j); * complementarity form model transport / supply_con.m_supply, demand_con.m_demand, deliver_con.x /; solve transport using mcp;