Ault Food Limited11 is planning the production and distribution system for its new line of food products. Plants may be opened at any of sites i = 1,

c, 7, and warehouses at locations j = 1,

c, 13, to meet demands dk at customer regions k = 1,

c, 219. Each plant costs $50 million to open and produces up to 30 thousand cases per year. Warehouses cost $12 million to open and handle up to 10 cases per year. Transportation costs are ri,j per case for rail shipment from plant i to warehouse j, and tj,k per case for trucking from warehouse j to customer k. No direct shipments from the plants are allowed. Formulate ILP model to decide which facilities to open and how to service customers using the decision variables

(i = 1,

c, 7; j = 1,

c, 13; k = 1,

c, 219)

xi,j,k ! thousand of cases produced at plant i and shipped to customer k via warehouse j yi ! e 1 if plant i is opened 0 otherwise wi ! e 1 if warehouse j is opened 0 otherwise