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A B C D E F G H
Unit Cost Destination
1 2 3
1$9 $6 $8
Source 2 $7 $12 $10
3$6 $7 $6
Shipments Destination
1 2 3 Total Shipped Supply
1 0 2 2 4 = 4
Source 2 3 0 0 3 = 3
3 1 0 1 2 = 2
Total Received 4 2 3
= = = Total Cost
Demand 4 2 3 $61
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A B C D E F G H I
Unit Cost
1 2 3 4
1$3 $7 $6 $4
Source 2 $2 $4 $3 $2
3$4 $3 $8 $5
Shipments
1 2 3 4 Total Shipped Supply
1 3 0 0 2 5 = 5
Source 2 0 0 2 0 2 = 2
3 0 3 0 0 3 = 3
Total Received 3 3 2 2
= = = = Total Cost
Demand 3 3 2 2 $32
Destination
Destination
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25
Distance (miles)
1 2 3 4
1800 1,300 400 700
Plant 2 1,100 1,400 600 1,000
3600 1,200 800 900
Fixed Cost $100
Cost per Mile $0.50
Unit Cost
1 2 3 4
1$500 $750 $300 $450
Plant 2 $650 $800 $400 $600
3$400 $700 $500 $550
Shipments
1 2 3 4 Total Shipped Supply
1 0 0 2 10 12 =12
Plant 2 0 9 8 0 17 =17
310 1 0 0 11 =11
Total Received 10 10 10 10
= = = = Total Cost
Demand 10 10 10 10 $20,200
Distribution Center
Distribution Center
Distribution Center
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A B C D E F G
Unit Cost
Today Tomorrow
Source Dick $3.00 $2.70
Harry $2.90 $2.80
Purchases
Today Tomorrow Total Supply
Source Dick 0 4 4 <= 5
Harry 3 0 3 <= 4
Total Received 3 4
= = Total Cost
Demand 3 4 $19.50
Destination
Destination
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A B C D E F G H
Unit Cost Product
1 2 3
1$31 $45 $38
2$29 $41 $35
Plant 3 $32 $46 $40
4$28 $42 —
5$29 $43 —
Production Product
1 2 3 Total Supply
1 0 0 200 200 <= 400
2 0 0 600 600 <= 600
Plant 3 0 0 0 0 <= 400
4600 0 0 600 <= 600
5 0 1000 01000 <= 1,000
Total 600 1000 800
= = = Total Cost
Demand 600 1,000 800 $88,400
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A B C D E F G H
Labor Hours / Acre
Wheat Barley Oats
England 18 15 12
France 13 12 10
Spain 16 12 16
Labor Cost / Hour
Wheat Barley Oats
England $9.00 $8.10 $6.90
France $7.20 $9.00 $7.50
Spain $9.90 $8.40 $6.30
Cost/Acre
Wheat Barley Oats
England $162.00 $121.50 $82.80
France $93.60 $108.00 $75.00
Spain $158.40 $100.80 $100.80
Land Allocation (millions of acres)
Wheat Barley Oats Total Supply
England 0 0 70 70 =70
France 110 0 0 110 =110
Spain 15 60 580 =80
Total 125 60 75
= = = Total Cost ($millions)
Demand 125 60 75 25,020
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A B C D E F G H
Hauling Cost Site Price
1 2 3 per Ton
Pit North $30 $60 $50 $100
South $60 $30 $40 $120
Unit Cost Site
1 2 3
Pit North $130 $160 $150
South $180 $150 $160
Gravel Hauled Site
1 2 3 Total Supply
Pit North 10 0 8 18 <= 18
South 0 5 2 7 <= 14
Total Received 10 510
= = = Total Cost
Demand 10 510 $3,570
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A B C D E F G H I J K L M
P&T Co. Distribution Problem
Unit Cost Destination (Warehouse) Range Name Cells
Sacramento Salt Lake City Rapid City Albuquerque Demand D17:G17
Source Bellingham $464 $513 $654 $867 ShipmentQuantity D12:G14
(Cannery) Eugene $352 $416 $690 $791 Supply J12:J14
Albert Lea $995 $682 $388 $685 TotalCost J17
TotalReceived D15:G15
TotalShipped H12:H14
Shipment Quantity Destination (Warehouse) UnitCost D5:G7
(Truckloads) Sacramento Salt Lake City Rapid City Albuquerque Total Shipped Supply
Source Bellingham 0 20 055 75 =75
(Cannery) Eugene 80 45 0 0 125 =125
Albert Lea 0 0 70 30 100 =100
Total Received 80 65 70 85
= = = = Total Cost
Demand 80 65 70 85 $152,535
Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$D$12 Bellingham Sacramento 0 15 464 1E+30 15
$E$12 Bellingham Salt Lake City 20 0513 15 21
$F$12 Bellingham Rapid City 0 84 654 1E+30 84
$G$12 Bellingham Albuquerque 55 0867 21 351
$D$13 Eugene Sacramento 80 0352 15 1E+30
$E$13 Eugene Salt Lake City 45 0416 21 15
$F$13 Eugene Rapid City 0 217 690 1E+30 217
$G$13 Eugene Albuquerque 0 21 791 1E+30 21
$D$14 Albert Lea Sacramento 0 728 995 1E+30 728
$E$14 Albert Lea Salt Lake City 0 351 682 1E+30 351
$F$14 Albert Lea Rapid City 70 0388 84 1E+30
$G$14 Albert Lea Albuquerque 30 0685 351 84
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$D$15 Total Received Sacramento 80 -418 80 45 0
$E$15 Total Received Salt Lake City 65 -354 65 55 0
$F$15 Total Received Rapid City 70 -297 70 30 0
$G$15 Total Received Albuquerque 85 085 0 1E+30
$H$12 Bellingham Total Shipped 75 867 75 055
$H$13 Eugene Total Shipped 125 770 125 045
$H$14 Albert Lea Total Shipped 100 685 100 030
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A B C D E F G H I J K L
Metro Water District Distribution Problem
Unit Cost ($millions) Berdoo Los Devils San Go Hollyglass Range Name Cells
Colombo River 160 130 220 170 Available I11:I13
Sacron River 140 130 190 150 Needed C16:F16
Calorie River 190 200 230 – TotalCost I17
TotalFromRiver G11:G13
TotalToCity C14:F14
Water Distribution Total UnitCost C4:F6
(million acre-feet) Berdoo Los Devils San Go Hollyglass From River Available WaterDistribution C11:F13
Colombo River 0 5 0 0 5 <= 5
Sacron River 2 0 2.5 1.5 6 <= 6
Calorie River 0 0 1.5 0 1.5 <= 5
Total To City 2 5 4 1.5
= = = = Total Cost
Needed 2 5 4 1.5 ($million)
1,975
Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$C$11 Colombo River Berdoo 0 0 160 1E+30 0
$D$11 Colombo River Los Devils 5 0 130 20 1E+30
$E$11 Colombo River San Go 0 10 220 1E+30 10
$F$11 Colombo River Hollyglass 0 0 170 020
$C$12 Sacron River Berdoo 2 0 140 0 1E+30
$D$12 Sacron River Los Devils 0 20 130 1E+30 20
$E$12 Sacron River San Go 2.5 0190 10 10
$F$12 Sacron River Hollyglass 1.5 0150 20 0
$C$13 Calorie River Berdoo 0 10 190 1E+30 10
$D$13 Calorie River Los Devils 0 50 200 1E+30 50
$E$13 Calorie River San Go 1.5 0230 10 20
$F$13 Calorie River Hollyglass 0 -190 0 1E+30 190
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$C$14 Total To City Berdoo 2 180 22.5 1.5
$D$14 Total To City Los Devils 5 150 5 0 1.5
$E$14 Total To City San Go 4 230 43.5 1.5
$F$14 Total To City Hollyglass 1.5 190 1.5 2.5 1.5
$G$11 Colombo River From River 5 -20 5 1.5 0
$G$12 Sacron River From River 6 -40 6 1.5 2.5
$G$13 Calorie River From River 1.5 0 5 1E+30 3.5
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A B C D E F G H I J K L
Metro Water District Distribution Problem
Unit Cost ($millions) Berdoo Los Devils San Go Hollyglass Range Name Cells
Colombo River 160 130 220 170 Available I11:I13
Sacron River 140 130 190 150 Maximum C19:F19
Calorie River 190 200 230 – Minimum C15:F15
TotalCost I17
TotalFromRiver G11:G13
Water Distribution Total TotalToCity C17:F17
(million acre-feet) Berdoo Los Devils San Go Hollyglass From River Available UnitCost C4:F6
Colombo River 0 5 0 0 5 = 5 WaterDistribution C11:F13
Sacron River 2.5 2 0 1.5 6 = 6
Calorie River 1 0 4 0 5 = 5
Minimum 2 5 4 1.5
<= <= <= <= Total Cost
Total To City 3.5 7 4 1.5 ($million)
<= <= <= <= 2,595
Maximum 4 7 6 3.5
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A B C D E F G H I
Unit Profit
1 2 3 4
1$800 $700 $500 $200
Plant 2 $500 $200 $100 $300
3$600 $400 $300 $500
Shipments
1 2 3 4 Total Shipped Supply
1 0 60 0 0 60 =60
Plant 2 40 0 0 40 80 =80
3 0 0 20 20 40 =40
Total Received 40 60 20 60
= = >= Total Cost
Commitment 40 60 20 $90,000
Customer
Customer