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(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. (Let Detroit be node 1, Los Angeles be node 2, Austin be node 3, Iowa be node 4, Maryland be node 5, Idaho be node 6, Arkansas be node 7, Just Sports be node 8, Sports Stuff be node 9, and Sports Dude be node 10. Express your answers in the form x,, where x,, represents the number of units shipped from node i to node j.) Min s.t. Detroit Production Los Angeles Production Austin Production Iowa Shipments Maryland Shipments Idaho Shipments Arkansas Shipments Iowa Processing Maryland Processing Idaho Processing Arkansas Processing Just Sports Demand Sports Stuff Demand Sports Dude Demand xij≥0 for all / and J. What is the optimal production strategy and shipping pattern for Sports of All Sorts? Enter the number of units shipped where x₁, represents the number of units shipped from node i to node j. X14 X15 X16 X17 X24 25 26 27 X34 35 36 37 X48 X58 X68 X78 X49 X59 X69 X79 X410 X510 X610 X710 What is the minimum attainable transportation cost (in dollars)? $ (c) Sports of All Sorts is considering expansion of the Iowa DC capacity to 800 units per week. The annual amortized cost of expansion is $40,000. Should the company expand the Iowa DC capacity so that it can process 800 skateboards per week? (Assume 50 operating weeks per year.) The cost of the optimal solution associated with this increased capacity at the Iowa distribution center is $ is 50 x ($[ $ --Select- expand. per year. The $40,000 cost of expansion --Select--- per week. Therefore, the potential savings over 50 weeks the potential savings, so Sports of All Sorts

(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. (Let Detroit be node 1, Los Angeles be node 2, Austin be node 3, Iowa be node 4, Maryland be node 5, Idaho be node 6, Arkansas be node 7, Just Sports be node 8, Sports Stuff be node 9, and Sports Dude be node 10. Express your answers in the form x,, where x,, represents the number of units shipped from node i to node j.) Min s.t. Detroit Production Los Angeles Production Austin Production Iowa Shipments Maryland Shipments Idaho Shipments Arkansas Shipments Iowa Processing Maryland Processing Idaho Processing Arkansas Processing Just Sports Demand Sports Stuff Demand Sports Dude Demand xij≥0 for all / and J. What is the optimal production strategy and shipping pattern for Sports of All Sorts? Enter the number of units shipped where x₁, represents the number of units shipped from node i to node j. X14 X15 X16 X17 X24 25 26 27 X34 35 36 37 X48 X58 X68 X78 X49 X59 X69 X79 X410 X510 X610 X710 What is the minimum attainable transportation cost (in dollars)? $ (c) Sports of All Sorts is considering expansion of the Iowa DC capacity to 800 units per week. The annual amortized cost of expansion is $40,000. Should the company expand the Iowa DC capacity so that it can process 800 skateboards per week? (Assume 50 operating weeks per year.) The cost of the optimal solution associated with this increased capacity at the Iowa distribution center is $ is 50 x ($[ $ --Select- expand. per year. The $40,000 cost of expansion --Select--- per week. Therefore, the potential savings over 50 weeks the potential savings, so Sports of All Sorts

Practical Management Science
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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(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. (Let Detroit be node 1, Los Angeles be node 2, Austin be node 3, Iowa be node 4, Maryland be node 5, Idaho be node 6, Arkansas be node 7, Just Sports be node 8, Sports Stuff be node 9, and Sports Dude be node 10. Express your answers in the form X;; where x¡; represents the number of units shipped from node i to node j.) Xij Min s.t. Detroit Production Los Angeles Production Austin Production Iowa Shipments Maryland Shipments Idaho Shipments Arkansas Shipments Iowa Processing Maryland Processing Idaho Processing Arkansas Processing Just Sports Demand Sports Stuff Demand Sports Dude Demand Xij ≥ 0 for all i and j. What is the optimal production strategy and shipping pattern for Sports of All Sorts? Enter the number of units shipped where x₁, represents the number of units shipped from node i to node j. Xij X14 15 16 17 X24 X25 X26 X27 x34 X35 36 37 X48 X58 X68 X78 X49 X59 X69 X79 X410 X510 X610 X710 NUMUGOVO = 00000 What is the minimum attainable transportation cost (in dollars)? $ is 50 x $ (c) Sports of All Sorts is considering expansion of the Iowa DC capacity to 800 units per week. The annual amortized cost of expansion is $40,000. Should the company expand the Iowa DC capacity so that it can process 800 skateboards per week? (Assume 50 operating weeks per year.) The cost of the optimal solution associated with this increased capacity at the Iowa distribution center is $ × ( $ [ ---Select--- expand. = per year. The $40,000 cost of expansion ---Select--- per week. Therefore, the potential savings over 50 weeks ✓the potential savings, so Sports of All Sorts
Transcribed Image Text:(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. (Let Detroit be node 1, Los Angeles be node 2, Austin be node 3, Iowa be node 4, Maryland be node 5, Idaho be node 6, Arkansas be node 7, Just Sports be node 8, Sports Stuff be node 9, and Sports Dude be node 10. Express your answers in the form X;; where x¡; represents the number of units shipped from node i to node j.) Xij Min s.t. Detroit Production Los Angeles Production Austin Production Iowa Shipments Maryland Shipments Idaho Shipments Arkansas Shipments Iowa Processing Maryland Processing Idaho Processing Arkansas Processing Just Sports Demand Sports Stuff Demand Sports Dude Demand Xij ≥ 0 for all i and j. What is the optimal production strategy and shipping pattern for Sports of All Sorts? Enter the number of units shipped where x₁, represents the number of units shipped from node i to node j. Xij X14 15 16 17 X24 X25 X26 X27 x34 X35 36 37 X48 X58 X68 X78 X49 X59 X69 X79 X410 X510 X610 X710 NUMUGOVO = 00000 What is the minimum attainable transportation cost (in dollars)? $ is 50 x $ (c) Sports of All Sorts is considering expansion of the Iowa DC capacity to 800 units per week. The annual amortized cost of expansion is $40,000. Should the company expand the Iowa DC capacity so that it can process 800 skateboards per week? (Assume 50 operating weeks per year.) The cost of the optimal solution associated with this increased capacity at the Iowa distribution center is $ × ( $ [ ---Select--- expand. = per year. The $40,000 cost of expansion ---Select--- per week. Therefore, the potential savings over 50 weeks ✓the potential savings, so Sports of All Sorts
Sports of All Sorts produces, distributes, and sells high-quality skateboards. Its supply chain consists of three factories (located in Detroit, Los Angeles, and Austin) that produce skateboards. The Detroit and Los Angeles facilities can produce 350 skateboards per week, but the Austin plant is larger and can produce up to 700 skateboards per week. Skateboards must be shipped from the factories to one of four distribution centers, or DCs (located in Iowa, Maryland, Idaho, and Arkansas). Each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week. Factory/DCs Detroit Los Angeles Austin 1 2 3 Retailers/DCS Just Sports Sports 'N Stuff Iowa The Sports Dude 25.00 35.00 40.00 8 Shipping Costs ($ per skateboard) 5 9 Iowa 30.00 27.50 Maryland 30.00 25.00 4 45.00 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. Maryland 20.00 Idaho 32.50 35.00 40.00 35.00 42.50 6 Shipping Costs ($ per skateboard) 5 Idaho 35.00 Arkansas 40.00 32.50 40.00 42.50 6 32.50 7 Arkansas 27.50 25.00 42.50 (a) Draw the network representation for this problem. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen
Transcribed Image Text: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. Factory/DCs Detroit Los Angeles Austin 1 2 3 Retailers/DCS Just Sports Sports 'N Stuff Iowa The Sports Dude 25.00 35.00 40.00 8 Shipping Costs ($ per skateboard) 5 9 Iowa 30.00 27.50 Maryland 30.00 25.00 4 45.00 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. Maryland 20.00 Idaho 32.50 35.00 40.00 35.00 42.50 6 Shipping Costs ($ per skateboard) 5 Idaho 35.00 Arkansas 40.00 32.50 40.00 42.50 6 32.50 7 Arkansas 27.50 25.00 42.50 (a) Draw the network representation for this problem. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen
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