Milford Lumber Company ships construction materials from three wood-processing plants to three retail stores. The shipping cost, monthly production capacities, and monthlydemand for framing lumber are given below.Plant12Store A$4.40$6.003$4.80Demand300Formulate a linear optimization model for this problem, implement your model on a spreadsheet, and use Excel Solver to find a solution that minimizes total distribution costs.If the constant is equal to one, enter "1".Let:X11 = number of components produced in Plant 1 and supplied to Store AX12 = number of components produced in Plant 1 and supplied to Store BX13 = number of components produced in Plant 1 and supplied to Store CX21 = number of components produced in Plant 2 and supplied to Store AX22 = number of components produced in Plant 2 and supplied to Store BX23 = number of components produced in Plant 2 and supplied to Store CX31 = number of components produced in Plant 3 and supplied to Store AX32 = number of components produced in Plant 3 and supplied to Store BX33 = number of components produced in Plant 3 and supplied to Store CStore B$7.80$7.10$4.60530Store C$6.10$3.90$3.90350Capacity280480450 MinX11 +X32 +Subject to the constraintsX11 +X21 +X31 +X33X11 +X12 +X13 +X12 +X13 +X21 +X13 -Select-vX23 -Select-vX33 -Select-X31 -Select-X32 -Select-X22 +X23 +X12 +X22 +X32 +X21 +X22 +X23 +X33 -Select-X11, X12, X13, X21, X22, X23, X31, X32, X33 ≥ 0What is the value of total distribution costs at the optimal solution? Use the Excel solver to find the optimal solution. Round your answer to the nearest dollar.$X31 +

The shipping cost($) from Plants to Stores is given above.

Answered: Milford Lumber Company ships…

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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Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?
Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.
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 How is Ski Butternut applying behavioristic variables in its segmentation strategy? Explain your answer.
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Can you guess the results of a sensitivity analysis on the initial inventory in the Pigskin model? See if your guess is correct by using SolverTable and allowing the initial inventory to vary from 0 to 10,000 in increments of 1000. Keep track of the values in the decision variable cells and the objective cell.
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?
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. As indicated by the algebraic formulation of the Pigskin model, there is no real need to calculate inventory on hand after production and constrain it to be greater than or equal to demand. An alternative is to calculate ending inventory directly and constrain it to be nonnegative. Modify the current spreadsheet model to do this. (Delete rows 16 and 17, and calculate ending inventory appropriately. Then add an explicit non-negativity constraint on ending inventory.)
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Modify the Pigskin model so that there are eight months in the planning horizon. You can make up reasonable values for any extra required data. Dont forget to modify range names. Then modify the model again so that there are only four months in the planning horizon. Do either of these modifications change the optima] production quantity in month 1?
The following table presents cost, capacity, and demand data for a transportation problem in Stephanie Robbin’s furniture company. Set up the appropriate transportation table and find the optimal solution using Excel's solver. From/To 1 2 3 Supply A 30 10 5 20 B 10 10 10 30 C 20 10 25 75 Demand 40 60 55 a. Is the problem balanced? [ Select ] ["Yes", "it is balanced", "No", "cannot determine"] , If not, where? [ Select ] ["Neither", "Supply", "Demand"] , and by how much? [ Select ] ["0", "40", "30", "25"] b. What is the optimal cost? $ [ Select ] ["2,500", "1,100", "1,275", "1,300"] c. Were you able to meet all demand requirement? [ Select ] ["no", "cannot determine based on the information given", "yes"] If not, which destination (s) was/were not met? [ Select ] ["none, all destinations were met based on supply and demand being equal", "destination 3 by 30 units", "destination 2 by 30 units", "destination 1 by 25 units…
Create spreadsheets and use Solver to determine the correct volumes to be produced to minimize cost for the following problem. Your company has two trucks that it wishes to use on a specific contract. One is a new truck the company is making payments on, and one is an old truck that is fully paid for. The new truck’s costs per mile are as follows: 54₵ (fuel/additives), 24₵ (truck payments), 36₵ (driver), 12₵ (repairs), and 1₵ (misc.). The old truck’s costs are 60₵ (fuel/additives), 0₵ (truck payments), 32₵ (rookie driver), 24₵ (repairs), and 1₵ (misc.). The company knows that truck breakdowns lose customers, so it has capped estimated repair costs at $14,000. The total distance involved is 90,000 miles (to be divided between the two trucks).
The Fish House (TFH) in Norfolk, Virginia, sells fresh fish and seafood. TFH receives daily shipments of farm-raised trout from a nearby supplier. Each trout costs $2.45 and is sold for $3.95. To maintain its reputation for freshness, at the end of the day TFH sells any leftover trout to a local pet food manufacturer for $1.25 each. The owner of TFH wants to determine how many trout to order each day. Historically, the daily demand for trout is: Demand 10 11 12 13 14 15 16 17 18 19 20 Probability 0.02 0.06 0.09 0.11 0.13 0.15 0.18 0.11 0.07 0.05 0.03 a. Construct a payoff matrix for this problem. b. How much should the owner of TFH be willing to pay to obtain a demand forecast that is 100% accurate? give a clear explanation for (b)
You work for the Brad's Nailer Company which manufactures three types of nailers: a pneumatic model, the "ProLine", and a cordless model. You have contracted to supply a national retail chain with all three models of nailers. However, Brad's nailer production capability is limited in three departments: production, testing, and packaging. The goal is to maximize your revenue. Your answer will be the number of ProLine nailers to be produced (The number of nailers may not be a whole number, which is acceptable in this chapter.) Use Scenario 3 Scenario 1 Scenario 2 Scenario 3 Pneum. Sales Price 38.50 Pneum. Prod Hrs 0.25 Pneum. Test Hrs 0.4 Pneum. Pkg Hrs 0.1 Pneum. Sales 18,000 ProLine Sales Price 59.95 ProLine Prod Hrs 0.4 ProLine Test Hrs 0.5 ProLine Pkg Hrs 0.1 ProLine Sales 5,750 Cordless Sales Price 49.50 Cordless Prod Hrs 0.3 Cordless Test Hrs 0.4 Cordless Pkg Hrs 0.1 Cordless Sales 12,000 Prod Hrs max 14,000 Testing Hrs max 19,000 Pkg Hrs max 4,500 46 0.25 0.4 0.1 21,000 71 0.3 0.5…

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