The 3J Company manufactures handbags, shoulder bags, and backpacks. The construction of the three products requires leather and synthetics, with leather being the limiting raw material. The production process uses two types of skilled labor: sewing and finishing. The following table gives the daily availability of the resources, their usage by the three products, and the prices per unit. Leather (ft³) Sewing (hr) Finishing (hr) Price in Pesos Hand bag 3 2 2 1200 Requirement per Unit Shoulder bag Backpack 4 3 2 2250 2 1.5 1 1100 Availability 45 43 47 a. Define the decision variables and formulate a linear programming model for this problem. b. Find the optimal solution using the Excel Solver and interpret the result. c. Determine the binding constraints.

The 3J Company manufactures handbags, shoulder bags, and backpacks. The construction of the three products requires leather and synthetics, with leather being the limiting raw material. The production process uses two types of skilled labor: sewing and finishing. The following table gives the daily availability of the resources, their usage by the three products, and the prices per unit. Leather (ft³) Sewing (hr) Finishing (hr) Price in Pesos Hand bag 3 2 2 1200 Requirement per Unit Shoulder bag Backpack 4 3 2 2250 2 1.5 1 1100 Availability 45 43 47 a. Define the decision variables and formulate a linear programming model for this problem. b. Find the optimal solution using the Excel Solver and interpret the result. c. Determine the binding constraints.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 73P

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Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?
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.
A plant has sufficient capacity to manufacture any combination of four different products (A, B, C, D). For each product, time is required to be invested in four different machines, which is expressed in hours per kilogram of product, as shown in the following table as shown in the following table: (attached image) Each machine has an availability of 60 hours per week. Products A, B, C and D can be sold at $9, $7, $6 and $5per kilo, respectively. Variable labor costs are $2 per hour for machines 1 and 2, and $3 per hour for machines 3 and 4. The material costs for each kilogram of product A are $4. The material costs for each kilogram of products B, C, D and D are $4 each kilogram of products B, C and D are $1. What needs to be done:Formulate a profit-maximizing PL model given the maximum demand per product shown in the table (there are 16 variables). Note: The picture is in spanish, but I mean... is pretty easy to understand
Brookside Tailors sells suits to three segments: Executive Custom, Signature, and Brookside One. Last year they had 6,000 Executive Custom, 15,550 Signature, and 38,200 Brookside One clients. The revenue they make annually from the three segments are as follows: $3500,$1800, and $600. The cost to serve these customers is as follows: $1000,$400, and $120, respectively. The retention rate for segments are 80%,76%, and 85%. Assuming an annual discount rate of 5%, please calculate the following: a. CLV for each segment. What is the total value of each segment? [6] b. Suppose the company decides that it would like to invest $2,500,000 next year on loyalty programs to increase the retention rate. How much would the retention rate need to increase to for each segment if the whole sum were spent in that segment? [6] c. Instead of spending on retention, let us say they are going to spend it to acquire more of customers. If they spend that amount of money, they anticipate targeting 2,000, 5000,…
Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows: Supplier Component 1 2 3 1 $12 $12 $15 2 $11 $10 $12 Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows: Supplier 1 2 3 Capacity 575 950 800 If the Edwards production plan for the next period includes 1050 units of component 1 and 775 units of component 2, what purchases do you recommend? That is, how many units of each component should be…
Weenies and Buns is a food processing plant which manufactures hot dogs and hot dog buns. They grind their own flour forthe hot dog buns at a maximum rate of 200 pounds per week. Eachhot dog bun requires 0.1 pound of flour. They currently have a contract with Pigland, Inc., which specifies that a delivery of 800pounds of pork product is delivered every Monday. Each hot dogrequires pound of pork product. All the other ingredients in thehot dogs and hot dog buns are in plentiful supply. Finally, the laborforce at Weenies and Buns consists of 5 employees working fulltime (40 hours per week each). Each hot dog requires 3 minutes oflabor, and each hot dog bun requires 2 minutes of labor. Each hotdog yields a profit of $0.80, and each bun yields a profit of $0.30.Weenies and Buns would like to know how many hot dogsand how many hot dog buns they should produce each week so asto achieve the highest possible profit.(a) Formulate a linear programming model for this problem.D,I (b) Use the…
The Morton Supply Company produces clothing, footwear, and accessories for dancing and gymnastics. They produce three models of pointe shoes used by ballerinas to balance on the tips of their toes. The shoes are produced from four materials: cardstock, satin, plain fabric, and leather. The number of square inches of each type of material used in each model of shoe, the amount of material available, and the profit/model are shown below: Material (measured in square inches) Model 1 Model 2 Model 3 Material Available Cardstock 12 10 14 1,200 Satin 24 20 15 2,000 Plain fabric 40 40 30 7,500 Leather 11 11 10 1,000 Profit per model $50 $44 $40 Identify the decision variables, objective function, and constraints in simple verbal statements. Mathematically formulate a linear optimization model. Please show Step 2 in Excel Note:- Do not provide handwritten solution. Maintain accuracy and…
The Morton Supply Company produces clothing, footwear, and accessories for dancing and gymnastics. They produce three models of pointe shoes used by ballerinas to balance on the tips of their toes. The shoes are produced from four materials: cardstock, satin, plain fabric, and leather. The number of square inches of each type of material used in each model of shoe, the amount of material available, and the profit/model are shown below: Material (measured in square inches) Model 1 Model 2 Model 3 Material Available Cardstock 12 10 14 1,200 Satin 24 20 15 2,000 Plain fabric 40 40 30 7,500 Leather 11 11 10 1,000 Profit per model $50 $44 $40 Identify the decision variables, objective function, and constraints in simple verbal statements. Mathematically formulate a linear optimization model.
A wood products firm uses leftover time at the end of each week to make goods for stock. Currently, there are two products on the list of items that are produced for stock: a chopping board and a knife holder. Both items require three operations: cutting, gluing, and finishing. The manager of the firm has collected the following data on these products: The manager has also determined that during each week 120 minutes are available for cutting, 650 minutes are available for gluing, and 360 minutes are available for finishing. Formulate Linear Programming (L.P) Model for above problem?
Kellpost Cereal Company sells four products: (1) Special L (a low-calorie, high-nutrition cereal); (2) Corn Bran (another low-calorie, high-nutrition cereal); (3) Admiral Smacks (a sugary cereal pitched at the children's market); and (4) Honey Pops (another sweet cereal pitched at the children's market). Kellpost has sufficient production capacity to produce a total of 10,000 boxes of cereal per month. For each of the past 16 months, Kellpost has kept track of the price and sales of each product. (These data are listed in the file P07_72.xlsx.) Market executives believe that Special L and Corn Bran might be substitutes for each other, as might be Admiral Smacks and Honey Pops. For example, this means that an increase in the price of Special L might raise the sales of Corn Bran. The variable cost of bringing a box of each cereal to market is as follows: Special L, $2.00; Corn Bran, $2.20; Admiral Smacks, $2.30; Honey Pops, $2.40. a. Use the given information to determine the price for…