Sports of All Sorts produces, distributes, and sells high-quality skateboards. Its supply chain consists of three factories located in Detroit, Los Angeles, and Austin, which produce skateboards. The Detroit and Los Angeles facilities can produce 350 skateboards per week, while the Austin plant can produce up to 700 skateboards per week. Skateboards must be shipped from the factories to one of four distribution centers, or DCs, located in Iowa, Maryland, Idaho, and Arkansas. Each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week.The first table shows the shipping costs per skateboard from the factories to the distribution centers:**Shipping Costs ($ per skateboard): Factories to DCs**| 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 |Skateboards are then shipped from the distribution centers to retailers. Sports of All Sorts supplies three major U.S. retailers: Just Sports, Sports 'N Stuff, and The Sports Dude. The weekly demands are 200 skateboards at Just Sports, 500 skateboards at Sports 'N Stuff, and 650 skateboards at The Sports Dude. The second table displays the per-unit costs for shipping skateboards between the DCs and the retailers:**Shipping Costs ($ per skateboard): Retailers to DCs**| 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 | 40.00 || The Sports Dude | 30.00| 40.00 | 32.50 | 42.50 | (b) 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. Node Assignments:- Detroit is node 1- Los Angeles is node 2- Austin is node 3- Iowa is node 4- Maryland is node 5- Idaho is node 6- Arkansas is node 7- Just Sports is node 8- Sports Stuff is node 9- Sports Dude is node 10Express your answers in the form $ x_{ij} $ where $ x_{ij} $ represents the number of units shipped from node $ i $ to node $ j $.**Objective:**Minimize [Text box for input]**Subject to Constraints:**1. Detroit Production: \[ -x_{14} + x_{15} + x_{16} + x_{17} \leq 350 \] (Displayed next to the constraint with a red "x" mark indicating error or restriction)2. Los Angeles Production: [Text box for input]3. Austin Production: [Text box for input]4. Iowa Shipments: [Text box for input]5. Maryland Shipments: [Text box for input]6. Idaho Shipments: [Text box for input]7. Arkansas Shipments: [Text box for input]8. Iowa Processing: [Text box for input]9. Maryland Processing: [Text box for input]10. Idaho Processing: [Text box for input]11. Arkansas Processing: [Text box for input]12. Just Sports Demand: [Text box for input]13. Sports Stuff Demand: [Text box for input]14. Sports Dude Demand: [Text box for input]Additional Requirement:\[x_{ij} \geq 0 \text{ for all } i \text{ and } j.\]

Sports of All Sorts produces, distributes, and sells high-quality skateboards. Its supply chain consists of three factories (located in Detroit, Los Angeles, and Austin) that produce skateboards. The Detroit and Los Angeles facilities can produce 350 skateboards per week, but the Austin plant is larger and can produce up to 700 skateboards per week. Skateboards must be shipped from the factories to one of four distribution centers, or DCs (located in Iowa, Maryland, Idaho, and Arkansas). Each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week. Shipping Costs ($ per skateboard) Maryland 50000 25.00 45.00 40.00 Factory/DCs Detroit Los Angeles 3 Austin Retailers/DCs Iowa Just Sports Sports 'N Stuff The Sports Dude 25.00 35.00 8 9 1 Iowa 40.00 Skateboards are then shipped from the distribution centers to retailers. Sports of All Sorts supplies three major U.S. retailers: Just Sports, Sports 'N Stuff, and The Sports Dude. The weekly demands are 200 skateboards at Just Sports, 500 skateboards at Sports 'N Stuff, and 650 skateboards at The Sports Dude. The following tables display the per-unit costs for shipping skateboards between the factories and DCs and for shipping between the DCs and the retailers. 30.00 27.50 30.00 4 Maryland 20.00 Idaho 32.50 35.00 40.00 35.00 6 42.50 Shipping Costs ($ per skateboard) 6 Idaho 35.00 Arkansas 40.00 40.00 32.50 42.50 32.50 7 Arkansas 27.50 25.00 42.50 7

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...