**Shipping Network Analysis for Mantastic Devices**Mantastic Devices designs and manufactures high-end support garments for men. The facilities in Manhattan and Atlanta serve as design and component manufacturing facilities. Components are then shipped to warehouses in Philadelphia or Knoxville, where they are held until final assembly is completed at either Memphis, New Orleans, or El Paso. Manufacturing capacity in Manhattan and Atlanta is 800 units. Demand at Memphis, New Orleans, and El Paso is 450, 490, and 650, respectively. The network representing the shipping routes is shown below.**Network Diagram:**- Nodes: - 1: Manhattan - 2: Atlanta - 3: Philadelphia - 4: Knoxville - 5: Memphis - 6: New Orleans - 7: El Paso- Direct shipping routes are indicated by arrows between nodes, with corresponding costs shown in the table below.**Shipping Costs Table:**- Costs for shipping between each facility are shown in the table. A blank cell indicates shipping between two facilities is not permitted.| | Philadelphia | Knoxville | Memphis | New Orleans | El Paso ||---------------|--------------|-----------|---------|-------------|---------|| Manhattan | $5 | $25 | | | || Atlanta | $22 | $3 | | | || Philadelphia | | $4 | $20 | $30 | $40 || Knoxville | $4 | | $7 | $15 | $20 |**Questions:**i) **Objective Function:** - What is the objective function for the Mantastic problem? Use the notation $ x_{ij} $, where $ i $ and $ j $ correspond to the node numbers indicated in the diagram.ii) **Constraint for Philadelphia:** - What is the constraint for the transshipment node in Philadelphia for the Mantastic problem?

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1- Mantastic Devices designs and manufactures high-end support garments for men. The facilities in Manhattan and Atlanta serve as design and component manufacturing facilities. Components are then shipped to warehouses in Philadelphia or Knoxville, where they are held until final assembly is completed at either Memphis, New Orleans, or El Paso. Manufacturing capacity in Manhattan and Atlanta is 800 units. Demand at Memphis, New Orleans, and El Paso is 450, 490, and 650, respectively. The network representing the shipping routes is shown below. Menyhs Mahatten atehia Ne O The costs for shipping between each facility is shown below. A blank cell indicates that shipping between two facilities is not permitted. Memphis New Orleans El Paso Philadelphia $5 Knoxville $25 Manhattan Atlanta Philadelphia Knoxville $22 $3 $4 $20 $30 $40 $4 $7 $15 $20 i) What is the objective function for the Mantastic problem? Use the notation X, where i and / correspond to the node numbers indicated in the diagram.

1- Mantastic Devices designs and manufactures high-end support garments for men. The facilities in Manhattan and Atlanta serve as design and component manufacturing facilities. Components are then shipped to warehouses in Philadelphia or Knoxville, where they are held until final assembly is completed at either Memphis, New Orleans, or El Paso. Manufacturing capacity in Manhattan and Atlanta is 800 units. Demand at Memphis, New Orleans, and El Paso is 450, 490, and 650, respectively. The network representing the shipping routes is shown below. Menyhs Mahatten atehia Ne O The costs for shipping between each facility is shown below. A blank cell indicates that shipping between two facilities is not permitted. Memphis New Orleans El Paso Philadelphia $5 Knoxville $25 Manhattan Atlanta Philadelphia Knoxville $22 $3 $4 $20 $30 $40 $4 $7 $15 $20 i) What is the objective function for the Mantastic problem? Use the notation X, where i and / correspond to the node numbers indicated in the diagram.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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**Shipping Network Analysis for Mantastic Devices**

Mantastic Devices designs and manufactures high-end support garments for men. The facilities in Manhattan and Atlanta serve as design and component manufacturing facilities. Components are then shipped to warehouses in Philadelphia or Knoxville, where they are held until final assembly is completed at either Memphis, New Orleans, or El Paso. Manufacturing capacity in Manhattan and Atlanta is 800 units. Demand at Memphis, New Orleans, and El Paso is 450, 490, and 650, respectively. The network representing the shipping routes is shown below.

**Network Diagram:**
- Nodes:
- 1: Manhattan
- 2: Atlanta
- 3: Philadelphia
- 4: Knoxville
- 5: Memphis
- 6: New Orleans
- 7: El Paso
- Direct shipping routes are indicated by arrows between nodes, with corresponding costs shown in the table below.

**Shipping Costs Table:**
- Costs for shipping between each facility are shown in the table. A blank cell indicates shipping between two facilities is not permitted.

| | Philadelphia | Knoxville | Memphis | New Orleans | El Paso |
|---------------|--------------|-----------|---------|-------------|---------|
| Manhattan | $5 | $25 | | | |
| Atlanta | $22 | $3 | | | |
| Philadelphia | | $4 | $20 | $30 | $40 |
| Knoxville | $4 | | $7 | $15 | $20 |

**Questions:**

i) **Objective Function:**
- What is the objective function for the Mantastic problem? Use the notation $ x_{ij} $, where $ i $ and $ j $ correspond to the node numbers indicated in the diagram.

ii) **Constraint for Philadelphia:**
- What is the constraint for the transshipment node in Philadelphia for the Mantastic problem?

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