please write a clear answer for each part of the question **Supply Chain and Distribution Analysis for Sports of All Sorts Skateboards****Overview:**Sports of All Sorts is a company specializing in the production and sale of high-quality skateboards. The supply chain management includes three primary factories and four distribution centers (DCs) across the United States. This analysis provides detailed information on the shipping costs associated with moving skateboards from factories to distribution centers and from distribution centers to major retailers.**Factories and Shipping to Distribution Centers:**The company maintains factories in three locations: Detroit, Los Angeles, and Austin. The production capacities for these factories are as follows:- Detroit and Los Angeles can each produce 350 skateboards per week.- Austin is a larger facility capable of producing 700 skateboards per week.The skateboards are transported to four distribution centers: Iowa, Maryland, Idaho, and Arkansas. Each DC is equipped to handle up to 500 skateboards per week.**Shipping Costs from Factories to Distribution Centers (per skateboard):**| **Factory/DCs** | **Iowa** | **Maryland** | **Idaho** | **Arkansas** ||-----------------|----------|--------------|-----------|--------------|| Detroit | $25.00 | $25.00 | $35.00 | $40.00 || Los Angeles | $35.00 | $45.00 | $35.00 | $42.50 || Austin | $40.00 | $40.00 | $42.50 | $32.50 |**Distribution Centers and Shipping to Retailers:**The distribution centers supply skateboards to three major U.S. retailers:- Just Sports with a weekly demand of 200 skateboards.- Sports 'N Stuff requiring 500 skateboards weekly.- The Sports Dude with a demand for 650 skateboards per week.**Shipping Costs from Distribution Centers to Retailers (per skateboard):**| **Retailers/DCs** | **Iowa** | **Maryland** | **Idaho** | **Arkansas** ||-------------------|----------|--------------|-----------|--------------|| Just Sports | $30.00 | $20.00 | $35.00 | $27.50 || Sports 'N Stuff | $27.50 | $32.50 | $40.00 | $32.50 The image contains a logistics optimization problem and tables for entering data related to transportation costs and shipping strategies. Here is the transcription and detailed explanation:---**Objective:**Build a model to minimize the transportation cost of a logistics system that will deliver skateboards from the factories to the distribution centers and from the distribution centers to the retailers. - **Nodes:** - Detroit: Node 1 - Los Angeles: Node 2 - Austin: Node 3 - Iowa: Node 4 - Maryland: Node 5 - Idaho: Node 6 - Arkansas: Node 7 - Just Sports: Node 8 - Sports Stuff: Node 9 - Sports Dude: Node 10Express your answers in the form $ x_{ij} $ where $ x_{ij} $ represents the number of units shipped from node $ i $ to node $ j $.---**Constraints:** - **Minimize:** - [Blank for entering cost function]- **Subject to:** - Detroit Production: [Blank] - Los Angeles Production: [Blank] - Austin Production: [Blank] - Iowa Shipments: [Blank] - Maryland Shipments: [Blank] - Idaho Shipments: [Blank] - Arkansas Shipments: [Blank] - Iowa Processing: [Blank] - Maryland Processing: [Blank] - Idaho Processing: [Blank] - Arkansas Processing: [Blank] - Just Sports Demand: [Blank] - Sports Stuff Demand: [Blank] - Sports Dude Demand: [Blank]- $ x_{ij} \geq 0 $ for all $ i $ and $ j $.---**Optimization Objective:**Determine the optimal production strategy and shipping pattern for Sports of All Sorts. Enter the number of units shipped where $ x_{ij} $ represents the number of units shipped from node $ i $ to node $ j $.[Table for entering number of units for $ x_{14}, x_{15}, \ldots, x_{10} $]---**Cost:**- What is the minimum attainable transportation cost (in dollars)? - [Blank for entering cost]---**Expansion Consideration:****(c)** Sports of All Sorts is considering expansion of the Iowa DC capacity to 800 units per

Decision Variable: Suppose-xij represents the units shipped from node i to node j

Answered: please write a clear answer for each…

Business

Operations Management

please write a clear answer for each part of the question

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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