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Tri-State Manufacturing has three factories (1, 2, and 3) and three warehouses (A, B, and C). The following table shows the shipping costs between each factory and warehouse, the factory manufacturing capabilities (in thousands), and the warehouse capacities (in thousands). Management would like to keep the warehouses filled to capacity in order to generate demand. To Warehouse A Warehouse B Warehouse C From Factory 1 Factory 2 Factory 3 $6 $8 $11 Capacity 7 Write the objective function and the constraint in equations. Let X;;= 1,000s of units shipped from factory i to warehouse j, and so on. a) The objective function, for the LP model= Minimize Z= $6 ▼+$5 $8 +$10 $11+$14 Subject to: +$3 ▼+ +$8 ▼+ +$18 ▼ ▼ ▼ ▼ ▼ (shipping cost from factory 1) (shipping cost from factory 2) (shipping cost from factory 3) Warehouse A capacity utilization Warehouse B capacity utilization Warehouse C capacity utilization Factory 1 production capability Factory 2 production capability Factory 3 production capability non negativity condition For all X₁, 20 b) Using a computer software for solving LP, the optimal solution achieved is: Total shipping costs (in thousands) = $(enter your response as a whole number). $5 $10 $14 12 $3 $8 $18 5 Production Capability 6 8 10

Tri-State Manufacturing has three factories (1, 2, and 3) and three warehouses (A, B, and C). The following table shows the shipping costs between each factory and warehouse, the factory manufacturing capabilities (in thousands), and the warehouse capacities (in thousands). Management would like to keep the warehouses filled to capacity in order to generate demand. To Warehouse A Warehouse B Warehouse C From Factory 1 Factory 2 Factory 3 $6 $8 $11 Capacity 7 Write the objective function and the constraint in equations. Let X;;= 1,000s of units shipped from factory i to warehouse j, and so on. a) The objective function, for the LP model= Minimize Z= $6 ▼+$5 $8 +$10 $11+$14 Subject to: +$3 ▼+ +$8 ▼+ +$18 ▼ ▼ ▼ ▼ ▼ (shipping cost from factory 1) (shipping cost from factory 2) (shipping cost from factory 3) Warehouse A capacity utilization Warehouse B capacity utilization Warehouse C capacity utilization Factory 1 production capability Factory 2 production capability Factory 3 production capability non negativity condition For all X₁, 20 b) Using a computer software for solving LP, the optimal solution achieved is: Total shipping costs (in thousands) = $(enter your response as a whole number). $5 $10 $14 12 $3 $8 $18 5 Production Capability 6 8 10

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter5: Network Models
Section: Chapter Questions
Problem 67P
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Tri-State Manufacturing has three factories (1, 2, and 3) and three warehouses (A, B, and C). The following table shows the shipping costs between each factory and warehouse, the factory manufacturing capabilities (in thousands), and the warehouse capacities (in thousands). Management would like to keep the warehouses filled to capacity in order to generate demand. Minimize Z = Subject to: $6 $8 $11 Write the objective function and the constraint in equations. Let X;;= 1,000s of units shipped from factory i to warehouse j, and so on. .= a) The objective function, for the LP model = ▼ + $5 + $10 + $14 For all X;; 20 b) Using a computer software for solving Total shipping costs (in thousands) = $ + $3 + $8 ▼ + + $18 (shipping cost from factory 1) (shipping cost from factory 2) (shipping cost from factory 3) Warehouse A capacity utilization Warehouse B capacity utilization Warehouse C capacity utilization Factory 1 production capability Factory 2 production capability Factory 3 production capability non negativity condition To Warehouse A Warehouse B Warehouse C From Factory 1 Factory 2 Factory 3 Capacity LP, the optimal solution achieved is: (enter your response as a whole number). $6 $8 $11 7 $5 $10 $14 12 $3 $8 $18 5 Production Capability 6 8 10
Transcribed Image Text:Tri-State Manufacturing has three factories (1, 2, and 3) and three warehouses (A, B, and C). The following table shows the shipping costs between each factory and warehouse, the factory manufacturing capabilities (in thousands), and the warehouse capacities (in thousands). Management would like to keep the warehouses filled to capacity in order to generate demand. Minimize Z = Subject to: $6 $8 $11 Write the objective function and the constraint in equations. Let X;;= 1,000s of units shipped from factory i to warehouse j, and so on. .= a) The objective function, for the LP model = ▼ + $5 + $10 + $14 For all X;; 20 b) Using a computer software for solving Total shipping costs (in thousands) = $ + $3 + $8 ▼ + + $18 (shipping cost from factory 1) (shipping cost from factory 2) (shipping cost from factory 3) Warehouse A capacity utilization Warehouse B capacity utilization Warehouse C capacity utilization Factory 1 production capability Factory 2 production capability Factory 3 production capability non negativity condition To Warehouse A Warehouse B Warehouse C From Factory 1 Factory 2 Factory 3 Capacity LP, the optimal solution achieved is: (enter your response as a whole number). $6 $8 $11 7 $5 $10 $14 12 $3 $8 $18 5 Production Capability 6 8 10
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