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. Min s.t. Beginning Inventory Flow X16 x26 Quarter 1 Demand Flow x37 Quarter 1 Production Flow Quarter 2 Demand Flow x 48 50 Quarter 2 Production Flow Quarter 3 Demand Flow X59 X67 600 Quarter 4 Demand Flow X78 X89 300 Quarter 3 Production Flow Quarter 4 Production Flow 910 500 = $ 400 = $ Production Capacities = $ = $ = $ Ending Inventory Flow Xij ≥ 0 for all i, j. Solve the linear program to find the optimal solution. = $ = $ = $ Production Nodes = $ 2 Quarter 1 Production 3 Quarter 2 Production Beginning Inventory 4 Quarter 3 Production Quarter 4 Production Develop a linear programming model to minimize cost and meet demand exactly. (Let x; be the number of square yards of carpet which flows from node i to node j.) Production Cost Per Square Yard 0 2 5 Inventory Cost per Square Yard 3 3 Production (arcs) Demand Nodes Report the cost (in dollars) associated with the optimal solution. $ 6 Quarter 1 Demand 0.25 7 Quarter 2 Demand. 0.25 8 Quarter 3 Demand 0.25 9 Quarter 4 Demand 0.25 10 Ending Inventory 400 500 400 400 100 Demand
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. Min s.t. Beginning Inventory Flow X16 x26 Quarter 1 Demand Flow x37 Quarter 1 Production Flow Quarter 2 Demand Flow x 48 50 Quarter 2 Production Flow Quarter 3 Demand Flow X59 X67 600 Quarter 4 Demand Flow X78 X89 300 Quarter 3 Production Flow Quarter 4 Production Flow 910 500 = $ 400 = $ Production Capacities = $ = $ = $ Ending Inventory Flow Xij ≥ 0 for all i, j. Solve the linear program to find the optimal solution. = $ = $ = $ Production Nodes = $ 2 Quarter 1 Production 3 Quarter 2 Production Beginning Inventory 4 Quarter 3 Production Quarter 4 Production Develop a linear programming model to minimize cost and meet demand exactly. (Let x; be the number of square yards of carpet which flows from node i to node j.) Production Cost Per Square Yard 0 2 5 Inventory Cost per Square Yard 3 3 Production (arcs) Demand Nodes Report the cost (in dollars) associated with the optimal solution. $ 6 Quarter 1 Demand 0.25 7 Quarter 2 Demand. 0.25 8 Quarter 3 Demand 0.25 9 Quarter 4 Demand 0.25 10 Ending Inventory 400 500 400 400 100 Demand
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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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.
Min
s.t.
Beginning Inventory Flow
x26
Quarter 1 Demand Flow
X37
X48
50
Quarter 1 Production Flow
Quarter 2 Demand Flow
X59
600
Quarter 2 Production Flow
Quarter 3 Demand Flow
X67
300
Quarter 3 Production Flow
Quarter 4 Demand Flow
X78
500
Quarter 4 Production Flow
X89
X910
400
= $
Production
Capacities
Develop a linear programming model to minimize cost and meet demand exactly. (Let Xij
which flows from node i to node j.)
= $
= $
= $
= $
Ending Inventory Flow
≥ 0 for all i, j.
Solve the linear program to find the optimal solution.
X16
= $
= $
Production
Nodes
= $
= $
2
Quarter 1
Production
3
Quarter 2
Production
4
Quarter 3
Production
1
Beginning
Inventory
5
Quarter 4
Production
Production Cost
Per Square Yard
0
2
5
Inventory Cost
per Square Yard
3
3
Production
(arcs)
Report the cost (in dollars) associated with the optimal solution.
$
Demand
Nodes
6
Quarter 1
Demand
0.25
7
Quarter 2
Demand
0.25
8
Quarter 3
Demand
0.25
9
Quarter 4
Demand
0.25
10
Ending
Inventory
400
500
400
400
100
Demand
i
be the number of square yards of carpet
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