***please help with the incorrect answer****

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. Production Production Cost Demand Nodes Nodes Per Square Yard 6 Quater 1 6 Demand 0 Beginning 1 Inventory Beginning Inventory 50 400 Quater 1 Demand 2 2 Quarter 1 2 Production Quarter 1 Production 600 0.25 Quarter 2 3 Quarter 2 3 Production Quarter 2 Production 7 Demand 5 300 500 Quarter 2 Demand Inventory Cost per Square Yard 0.25 3 Quarter 3 4 Production Quarter 3 Production 8 Quarter 3 8 Demand Quarter 3 400 Demand 500 0.25 5 Quarter 4 5 Production 3 9 Quarter 4 9 Demand Quarter 4 400 Demand 400 Quarter 4 Production Quarter 4 5 Production Quarter 4 Production 3 400 Quarter 4 9 Demand Quarter 4 400 Demand 0.25 10 Ending 10 Inventory Ending Inventory 100 Production Production Demand Capacities (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.) Min *16 + 2x26 +5x37 + 3x48 + 3x59 +0.25x67 + 0.25x78 +0.25x89 x +0.25x910 s.t. Beginning Inventory Flow X16 = 50