Question: Develop a linear programming model to minimize cost. (Let x ij be the number of square yards of carpet which flows from node i to

Develop a linear programming model to minimize

Develop a linear programming model to minimize cost. (Let x_ij be the number of square yards of carpet which flows from node i to node j.)

Min 0x16+2x26+5x37+3x48+3x59+0.25x67+0.25x78+0.25x89+0.25x910 (right)

s.t.

Beginning Inventory Flow X16=50 (wrong)

Quarter 1 Production Flow X26600 (wrong)

Quarter 2 Production Flow X37300 (wrong)

Quarter 3 Production Flow X48500 (wrong)

Quarter 4 Production Flow X59400 (wrong)

Quarter 1 Demand Flow X16+X26X67=400 (wrong)

Quarter 2 Demand Flow X37+X67X78=500 (wrong)

Quarter 3 Demand Flow X48+X78X89=400 (wrong)

Quarter 4 Demand Flow X59+X89X910=400 (wrong)

Ending Inventory Flow X910=100 (wrong)

I just need help with the ones I got wrong (in bold). Thank you in advance!!

Production Production Cost Demand Nodes Per Square Yard Nodes 6 Quater 1 6 Demand 0 Beginning 1 Inventory Beginning Inventory 50 400 Quater 1 Demand 2 Quarter 1 2 Production Quarter 1 Production 600 0.25 3 Quarter 2 3 Production 5 300 Quarter 2 Production Quarter 2 7 Demand Quarter 2 500 Demand Inventory Cost per Square Yard 0.25 4 Quarter 3 4 Production Quarter 3 Production 3 500 Quarter 3 8 Demand Quarter 3 400 Demand 0.25 3 Quarter 4 5 Production Quarter 4 Production Quarter 4 9 Demand Quarter 4 400 Demand 400 0.25 10 Ending 10 Inventory Ending Inventory 100 Production Production Demand Capacities (arcs)

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