American Olean15 makes product families i = 1,

c, 10 of tile at plants p = 1,

c, 4 to meet demands di,k (square feet) at sales distribution points (SDPs) k = 1,

c, 120. Variable costs of production and transportation total ci,p,k per square foot to make tile of family i at plant p and ship to SDP k. Each plant can produce up to 100% of capacity, with ui,p being the capacity if plant p makes only group i. Management wants to find a minimum total cost way to meet demand.

(a) Formulate an LP model to compute an optimal plan in terms of the decision variables 1i = 1,

c, 10; p = 1,

c, 4;

k = 1, c,1202 xi,p,k ! fraction of capacity at plant p devoted to making tile family i for shipment to SDP k

(b) Show that your model can be viewed as a flow with gains of the transportation problem type by identifying sources, sinks, supplies, demands, arc gain multipliers, and arc costs.