Develop a linear programming model to minimize cost. (Let x, be the number of square yards of carpet which flows from node / to node j.) Min s.t. Beginning Inventory Flow Quarter 1 Production Flow Quarter 2 Production Flow Quarter 3 Production Flow Quarter 4 Production Flow Quarter 1 Demand Flow Quarter 2 Demand Flow Quarter 3 Demand Flow Quarter 4 Demand Flow Ending Inventory Flow x 20 for all i, J. Solve the linear program to find the optimal solution (in dollars). (X16 X26X371 X48 X591 X671 X78X89 X910) - with cost $

MARKETING 2018
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Chapter14: Marketing Channels And Supply Chain Management
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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
400
Production
Capacities
Production
Nodes
Beginning
1 Inventory
Beginning
Inventory
2
Quarter 1
2 Production
Quarter 1
Production
3
Quarter 2
3 Production
Quarter 2
Production
4
Quarter 3
4 Production.
Quarter 3
Production
5
Quarter 4
5 Production
Quarter 4
Production
Production Cost
Per Square Yard
0
2
5
Inventory Cost
per Square Yard
3
3
Production
(arcs)
Demand
Nodes
Quater 1
Demand
0.25
0.25
6
Quater 1
6 Demand
Quarter 2
Demand
0.25
7
Quarter 2
7 Demand
8
Quarter 3
Demand
0.25
400
8
Quarter 3
Demand.
9
Quarter 4
Demand
500
400
9
Quarter 4
Demand
400
10
Ending
10 Inventory
Ending
Inventory
100
Demand.
℗
Transcribed Image Text: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. 50 600 300 500 400 Production Capacities Production Nodes Beginning 1 Inventory Beginning Inventory 2 Quarter 1 2 Production Quarter 1 Production 3 Quarter 2 3 Production Quarter 2 Production 4 Quarter 3 4 Production. Quarter 3 Production 5 Quarter 4 5 Production Quarter 4 Production Production Cost Per Square Yard 0 2 5 Inventory Cost per Square Yard 3 3 Production (arcs) Demand Nodes Quater 1 Demand 0.25 0.25 6 Quater 1 6 Demand Quarter 2 Demand 0.25 7 Quarter 2 7 Demand 8 Quarter 3 Demand 0.25 400 8 Quarter 3 Demand. 9 Quarter 4 Demand 500 400 9 Quarter 4 Demand 400 10 Ending 10 Inventory Ending Inventory 100 Demand. ℗
Develop a linear programming model to minimize cost. (Let x,, be the number of square yards of carpet which flows from node/ to node j.)
Min
s.t.
Beginning Inventory Flow
Quarter 1 Production Flow
Quarter 2 Production Flow
Quarter 3 Production Flow
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 X48X591 X671 X781 X89X910) =
with cost $
Transcribed Image Text:Develop a linear programming model to minimize cost. (Let x,, be the number of square yards of carpet which flows from node/ to node j.) Min s.t. Beginning Inventory Flow Quarter 1 Production Flow Quarter 2 Production Flow Quarter 3 Production Flow 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 X48X591 X671 X781 X89X910) = with cost $
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