Answer Happy

Contois Carpets is a small manufacturer of carpeting for home and office installations. Production capacity, demand, production cost per square yard (in dollars), and inventory holding cost per square yard (in dollars) for the next four quarters are shown in the network diagram below. 50 600 300 500 Production Nodes 1 Beginning 1 Inventory Beginning Inventory Quarter 1 2 Production Quarter 1 Production 3 Quarter 2 3 Production Quarter 2 Production 4 Quarter 3 4 Production Quarter 3 Production Production Cost Per Square Yard 0 2 5 Inventory Cost per Square Yard 3 Demand Nodes Quater 1 Demand 0.25 6 Quater 1 6 Demand 0.25 7 Quarter 2 Demand Quarter 2 Demand 400 8 Quarter 3 Demand 500 8 Quarter 3 Demand 400
Min 400 s.t. Production. Capacities Quarter 4 Production Beginning Inventory Flow Quarter 1 Production Flow 5 Quarter 4 5 Production Quarter 2 Production Flow Quarter 3 Production Flow 3 0.25 9 0.25 Production (arcs) Ⓡ Develop a linear programming model to minimize cost. (Let x; be the number of square yards of carpet which flows from node i to node j.) 9 Quarter 4. Demand. Quarter 4 Demand 400 10 Ending 10 Inventory Ending Inventory 100 Demand
Quarter 4 Production Flow Quarter 1 Demand Flow Quarter 2 Demand Flow Quarter 3 Demand Flow Quarter 4 Demand Flow Ending Inventory Flow xij≥0 for all i, j. Solve the linear program to find the optimal solution (in dollars). (X16X261 X371 X 481 X591 X671 X781 X89, X910) = with cost $