please write a clear answer for each part of the question 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)Factory/DCsDetroitLos AngelesAustin453Retailers/DCsJust SportsSports 'N StuffIowaThe Sports Dude25.0035.0040.001891Iowa30.0027.50Maryland30.0025.00Skateboards 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-unitcosts for shipping skateboards between the factories and DCs and for shipping between the DCs and the retailers.la45.0040.00Maryland20.00Idaho32.5035.0040.0035.0042.50Shipping Costs ($ per skateboard)56Idaho35.00Arkansas40.0040.0032.5042.5032.50Arkansas27.5025.0042.507 (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 Sportsbe node 8, Sports Stuff be node 9, and Sports Dude be node 10. Express your answers in the form xi; where xij represents the number of units shipped from node i to node j.)Mins.t.Detroit ProductionLos Angeles ProductionAustin ProductionIowa ShipmentsMaryland ShipmentsIdaho ShipmentsArkansas ShipmentsIowa ProcessingMaryland ProcessingIdaho ProcessingArkansas ProcessingJust Sports DemandSports Stuff DemandSports Dude Demandxij≥ 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 x;; represents the number of units shipped from node i to node j.X14 15 1617X24 25 26 27X34 35 36 37X48 X58 X68 X78X49 X59 X69 X79X410 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 $- $per week. Therefore, the potential savings over 50 weeks is 50 x× ( $ [per year. The $40,000 cost of expansion ---Select------Select---expand.$the potential savings, so Sports of All Sorts

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

Answered: please write a clear answer for each…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section6.5: Set-covering And Location-assignment Models

Problem 34P

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Located in the picturesque Berkshire Mountains of Western Massachusetts, Ski Butternut has been a family-owned, family-oriented ski destination for more than 50 years. The resort includes 22 trails for downhill skiing and snowboarding, two terrain parks for riding, and a dedicated area for snow tubing. Although Ski Butternut hosts some non-ski events during summer and fall, its business goes into high gear when snowy weather arrives, bringing skiers and riders from across Massachusetts, Connecticut, New York, and New Jersey. Matt Sawyer, Ski Butternuts director of marketing, says the primary target market has always been families with young children who are seeking affordable skiing. Everything from the snack-bar menus to the ski-shop merchandise is presented with families in mind. So that parents can have fun in the snow without worry, the resort has a Childrens Center for children who are too young to ski or have no interest. Fifth-graders are invited to ski for free when accompanied by an adult who buys an adult lift ticket. The resort also created two terrain parks for young snowboarders who were clamoring for a more exciting riding experience. Without the terrain parks, Sawyer says, these boarders would have asked their parents to take them to competing mountains in Vermont. Ski Butternuts research shows that first-timers are a particularly important segment, because they tend to have a strong allegiance to the resort where they learn to ski. First-timers typically visit the resort seven times before seeking out more challenging mountains. As a result, Ski Butternut has made teaching first-timers to ski or snowboard one of its specialties. For this market, the resort bundles ski or board rentals, lift tickets, and also offers a wide range of individual and group lessons for all ages and abilities at a value price. Because Ski Butternut has trails for different skill levels, beginners can challenge themselves by changing trails within the resort once they feel confident. Ski Butternut also targets seniors and college students. Knowing that weekends are the busiest period, the resort offers special midweek prices to attract seniors who have free time to ski on weekdays. College students are particularly value-conscious, and they often travel to ski resorts as a group. As a result, Ski Butternut offers weekend and holiday discounts to bring in large numbers of students who would otherwise ski elsewhere. Thanks to Facebook, Twitter, and other social media, students quickly spread the word about special pricing, which enhances Ski Butternuts ability to reach this key segment. In addition, the resort highlights discount pricing for families when targeting specific segments, such as scout troops, military personnel, emergency services personnel, and members of local ski clubs. Another segment Ski Butternut has selected for marketing attention is ski racers. The resort features professional coaching, lessons, and programs for ski racers in the age group of 8 to 20. Sawyer notes that these ski racers are extremely dedicated to training, which means theyre on the slopes as often as possible, a positive for the resorts attendance and revenue. To stay in touch with racers, Ski Butternut has a special website and a dedicated Facebook page. Sawyer conducts up to 1,200 customer surveys every year to better understand who his customers are and what they need. He also compares the results with skiers who visit mountains of a similar size in other areas. Digging deeper, he analyzes data drawn from the ski shops rental business to build a detailed picture of customers demographics, abilities, and preferences. Based on this research, he knows that the typical family at Ski Butternut consists of two children under age 18 who ski or ride, and at least one parent who skis. Because they can obtain so much information from and about their customers, Sawyer and his team are able to make better decisions about the marketing mix for each segment. By better matching the media with the audience, they get a better response from advertising, e-mail messages, and other marketing communications. As one example, they found that 15 percent of the visitors to Ski Butternuts website were using a smartphone to access the site. Sawyer has now created a special version of the site specifically for mobile use and created a text-message contest to engage skiers who have smartphones.16 Of the four categories of variables, which one seems to be the most central to Ski Butternuts segmentation strategy, and why?
Located in the picturesque Berkshire Mountains of Western Massachusetts, Ski Butternut has been a family-owned, family-oriented ski destination for more than 50 years. The resort includes 22 trails for downhill skiing and snowboarding, two terrain parks for riding, and a dedicated area for snow tubing. Although Ski Butternut hosts some non-ski events during summer and fall, its business goes into high gear when snowy weather arrives, bringing skiers and riders from across Massachusetts, Connecticut, New York, and New Jersey. Matt Sawyer, Ski Butternuts director of marketing, says the primary target market has always been families with young children who are seeking affordable skiing. Everything from the snack-bar menus to the ski-shop merchandise is presented with families in mind. So that parents can have fun in the snow without worry, the resort has a Childrens Center for children who are too young to ski or have no interest. Fifth-graders are invited to ski for free when accompanied by an adult who buys an adult lift ticket. The resort also created two terrain parks for young snowboarders who were clamoring for a more exciting riding experience. Without the terrain parks, Sawyer says, these boarders would have asked their parents to take them to competing mountains in Vermont. Ski Butternuts research shows that first-timers are a particularly important segment, because they tend to have a strong allegiance to the resort where they learn to ski. First-timers typically visit the resort seven times before seeking out more challenging mountains. As a result, Ski Butternut has made teaching first-timers to ski or snowboard one of its specialties. For this market, the resort bundles ski or board rentals, lift tickets, and also offers a wide range of individual and group lessons for all ages and abilities at a value price. Because Ski Butternut has trails for different skill levels, beginners can challenge themselves by changing trails within the resort once they feel confident. Ski Butternut also targets seniors and college students. Knowing that weekends are the busiest period, the resort offers special midweek prices to attract seniors who have free time to ski on weekdays. College students are particularly value-conscious, and they often travel to ski resorts as a group. As a result, Ski Butternut offers weekend and holiday discounts to bring in large numbers of students who would otherwise ski elsewhere. Thanks to Facebook, Twitter, and other social media, students quickly spread the word about special pricing, which enhances Ski Butternuts ability to reach this key segment. In addition, the resort highlights discount pricing for families when targeting specific segments, such as scout troops, military personnel, emergency services personnel, and members of local ski clubs. Another segment Ski Butternut has selected for marketing attention is ski racers. The resort features professional coaching, lessons, and programs for ski racers in the age group of 8 to 20. Sawyer notes that these ski racers are extremely dedicated to training, which means theyre on the slopes as often as possible, a positive for the resorts attendance and revenue. To stay in touch with racers, Ski Butternut has a special website and a dedicated Facebook page. Sawyer conducts up to 1,200 customer surveys every year to better understand who his customers are and what they need. He also compares the results with skiers who visit mountains of a similar size in other areas. Digging deeper, he analyzes data drawn from the ski shops rental business to build a detailed picture of customers demographics, abilities, and preferences. Based on this research, he knows that the typical family at Ski Butternut consists of two children under age 18 who ski or ride, and at least one parent who skis. Because they can obtain so much information from and about their customers, Sawyer and his team are able to make better decisions about the marketing mix for each segment. By better matching the media with the audience, they get a better response from advertising, e-mail messages, and other marketing communications. As one example, they found that 15 percent of the visitors to Ski Butternuts website were using a smartphone to access the site. Sawyer has now created a special version of the site specifically for mobile use and created a text-message contest to engage skiers who have smartphones.16 What role do geographic variables play in Ski Butternuts segmentation and targeting?
Located in the picturesque Berkshire Mountains of Western Massachusetts, Ski Butternut has been a family-owned, family-oriented ski destination for more than 50 years. The resort includes 22 trails for downhill skiing and snowboarding, two terrain parks for riding, and a dedicated area for snow tubing. Although Ski Butternut hosts some non-ski events during summer and fall, its business goes into high gear when snowy weather arrives, bringing skiers and riders from across Massachusetts, Connecticut, New York, and New Jersey. Matt Sawyer, Ski Butternuts director of marketing, says the primary target market has always been families with young children who are seeking affordable skiing. Everything from the snack-bar menus to the ski-shop merchandise is presented with families in mind. So that parents can have fun in the snow without worry, the resort has a Childrens Center for children who are too young to ski or have no interest. Fifth-graders are invited to ski for free when accompanied by an adult who buys an adult lift ticket. The resort also created two terrain parks for young snowboarders who were clamoring for a more exciting riding experience. Without the terrain parks, Sawyer says, these boarders would have asked their parents to take them to competing mountains in Vermont. Ski Butternuts research shows that first-timers are a particularly important segment, because they tend to have a strong allegiance to the resort where they learn to ski. First-timers typically visit the resort seven times before seeking out more challenging mountains. As a result, Ski Butternut has made teaching first-timers to ski or snowboard one of its specialties. For this market, the resort bundles ski or board rentals, lift tickets, and also offers a wide range of individual and group lessons for all ages and abilities at a value price. Because Ski Butternut has trails for different skill levels, beginners can challenge themselves by changing trails within the resort once they feel confident. Ski Butternut also targets seniors and college students. Knowing that weekends are the busiest period, the resort offers special midweek prices to attract seniors who have free time to ski on weekdays. College students are particularly value-conscious, and they often travel to ski resorts as a group. As a result, Ski Butternut offers weekend and holiday discounts to bring in large numbers of students who would otherwise ski elsewhere. Thanks to Facebook, Twitter, and other social media, students quickly spread the word about special pricing, which enhances Ski Butternuts ability to reach this key segment. In addition, the resort highlights discount pricing for families when targeting specific segments, such as scout troops, military personnel, emergency services personnel, and members of local ski clubs. Another segment Ski Butternut has selected for marketing attention is ski racers. The resort features professional coaching, lessons, and programs for ski racers in the age group of 8 to 20. Sawyer notes that these ski racers are extremely dedicated to training, which means theyre on the slopes as often as possible, a positive for the resorts attendance and revenue. To stay in touch with racers, Ski Butternut has a special website and a dedicated Facebook page. Sawyer conducts up to 1,200 customer surveys every year to better understand who his customers are and what they need. He also compares the results with skiers who visit mountains of a similar size in other areas. Digging deeper, he analyzes data drawn from the ski shops rental business to build a detailed picture of customers demographics, abilities, and preferences. Based on this research, he knows that the typical family at Ski Butternut consists of two children under age 18 who ski or ride, and at least one parent who skis. Because they can obtain so much information from and about their customers, Sawyer and his team are able to make better decisions about the marketing mix for each segment. By better matching the media with the audience, they get a better response from advertising, e-mail messages, and other marketing communications. As one example, they found that 15 percent of the visitors to Ski Butternuts website were using a smartphone to access the site. Sawyer has now created a special version of the site specifically for mobile use and created a text-message contest to engage skiers who have smartphones.16 How is Ski Butternut applying behavioristic variables in its segmentation strategy? Explain your answer.
Adirondack Paper Mills, Inc. operates paper plants in Augusta, Maine, andTupper Lake, New York. Warehouse facilities are located in Albany, New York, and Portsmouth, New Hampshire. Distributors are located in Boston, New York, and Philadelphia. The Augusta plant has a capacity of 300 units and the Tupper Lake plant has a capacity of 100 units. Boston has a demand of 150 units, New York has a demand of 100 units, and Philadelphia has a demand of 150 units. The unit transportation costs (in dollars) for shipments from the two plants to the two warehouses are presented in Table 4 and those from the two warehouses to the threedistributors are presented in Table 5. Table 4: Problem 1.10aPlant/Warehouse Albany PortsmouthAugusta 7 5Tupper Lake 3 4 Table 5: Problem 1.10bWarehouse/Distributor Boston New York PhiladelphiaAlbany…
A garment producer has three warehouses W1, W2, and W3. These warehouses have 30, 60, and 70 units of their items. Their five retail showrooms at R1, R2, R3, R4, and R5 need 35, 20, 40, 28, and 12 units respectively. Determine the optimum distribution cost. The transport cost in ($ per unit) between every warehouse and every retail showroom is presented in the below table: Warehouse Retail Showroom R1 R2 R3 R4 R5 W1 55 30 40 50 40 W2 35 30 100 45 60 W3 40 60 95 35 30
The Midlands Field Produce Company contracts with potato farmers in Colorado, Minnesota, North Dakota, and Wisconsin for monthly potato shipments. Midlands picks up the potatoes at the farms and ships mostly by truck (and sometimes by rail) to its sorting and distribution centers in Ohio, Missouri, and Iowa. At these centers the potatoes are cleaned, rejects are discarded, and the potatoes are sorted according to size and quality. They are then shipped to combination plants and distribution centers in Virginia, Pennsylvania, Georgia, and Texas, where the company produces a variety of potato products and distributes bags of potatoes to stores. Exceptions are the Ohio distribution center, which will accept potatoes only from farms in Minnesota, North Dakota, and Wisconsin, and the Texas plant, which won’t accept shipments from Ohio because of disagreements over delivery schedules and quality issues. Following are summaries of the shipping costs from the farms to the distribution centers…
World Foods, Inc., imports food products such as meats, cheese, and pastries to the United States from warehouses at ports in Hamburg, Marseilles, and Liverpool. Ships from these ports deliver the products to Norfolk, New York, and Savannah, where they are stored in company warehouses before being shipped to distribution centers in Dallas, St. Louis, and Chicago. The products are then distributed to specialty food stores and sold through catalogs. The shipping costs ($/1,000 lb.) from the European ports to the U.S. cities and the available supplies (1,000 lb.) at the European ports are provided in the following table: U.S. City European Port 4. Norfolk 5. New York 6. Savannah Supply 1. Hamburg $420 $390 $610 55 2. Marseilles 510 590 470 78 3. Liverpool 450 360 480 37 The transportation costs ($/1,000 lb.) from each U.S. city of the three distribution centers and the demands (1,000 lb.) at the distribution…
Pine Valley Furniture In an effort to better serve the various departments at Pine Valley Furniture, the PVF information systems department assigns one of its systems analysts to serve as a liaison to a particular business unit. Chris Martin is currently the liaison to the purchasing department. After graduating from Valley State University, Chris began working at Pine Valley Furniture. He began his career at PVF as a programmer/analyst I. This job assignment required him to code and maintain financial application systems in COBOL. In the six years he has been at PVF, he has been promoted several times; his most recent promotion was to a junior systems analyst position. During his tenure at PVF, Chris has worked on several important projects, including serving as a team member on a project that developed a five-year plan that would renovate the manufacturing information systems. Chris enjoys his work at Pine Valley Furniture and wishes to continue moving up the information systems…
Universal Exports has four factories where it makes potato mashers. These are sent to each of four retail outlets. The cost (in thousand pesos) of shipping a case from each source to each destination is given below. Each of the factories can produce 100 units while the demand at A is 80 units, B is 70 units, C is 120 units, and D is 100 units. How many units must be transported from Factory 1 to retail outlet D?
fertilizer manufacturer has to fulfill supply contracts to its two main customers (650 tons to Customer A and 800 tons to Customer B). It can meet this demand by shipping existing inventory from any of its three warehouses. Warehouse 1 (W1) has 400 tons of inventory onhand, Warehouse 2 (W2) has 500 tons, and Warehouse 3 (W3) has 600 tons. The company would like to arrange the shipping for the lowest cost possible, where the per-ton transit costs are as follows: W 1 W 2 W 3 Customer A $7.50 $6.25 $6.50 Customer B $6.75 $7.00 $8.00 Write the objective function and the constraint in equations. Let Vij= tons shipped to customer i from warehouse j, and so on. For example, VA1=tons shipped to customer A from warehouse W1. This exercise contains only parts b, c, d, e, and f. Part 2 b) The objective function for the LP model =
Solve the following problem: The Krampf Lines railway company specializes in coal handling. On Saturday, Krampf had empty cars at the following towns in the quantities indicated: Town Supply of cars Morgantown 35 Youngstown 60 Pitsburg 25 By Monday, the following towns will need cars as follows: Town Demand for cars Coal Valley 30 Coal town 45 Coal junction 25 Coalsburg 20 The result is shown in the table below. To From Coal Valley Coal town Coal junction Coalsburg Morgantown 50 30 60 70 Youngstown 20 80 10 90 Pitsburg 100 40 80 30 Required: Minimize total miles over which cars are moved to new locations regarding the following: Formulate as a linear programming. Use North-West corner method to obtain the total shipment cost of coal cars.
A city has two high schools. The first school has a maximum enrollment of 900 students and the second school has a maximum enrollment of 550 students. The city is divided into two regions: Inner City and Suburbs. There are at least 500 students in the Inner City region and at least 800 students in the Suburbs region. The annual transportation cost varies by region as shown in the table.

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