A contractor builds three types of houses: the Aries, the Belfair, and the Wexford. Each house requires one lot, and the following table gives the number of labor-hours and the amount of capital needed for each type of house, as well as the profit on the sale of each house. There are 9 lots, 36,400 labor-hours, and $2,574,200 available for the contractor's use. Aries Belfair Wexford Labor-hours 3,000 3,700 5,000 Capital $205,000 $279,600 $350,000 Profit $20,000 $25,000 $30,000 (a) Building how many of each type of house will maximize his profit? Aries houses Belfair houses Wexford houses (b) What is the maximum possible profit?

A contractor builds three types of houses: the Aries, the Belfair, and the Wexford. Each house requires one lot, and the following table gives the number of labor-hours and the amount of capital needed for each type of house, as well as the profit on the sale of each house. There are 9 lots, 36,400 labor-hours, and $2,574,200 available for the contractor's use. Aries Belfair Wexford Labor-hours 3,000 3,700 5,000 Capital $205,000 $279,600 $350,000 Profit $20,000 $25,000 $30,000 (a) Building how many of each type of house will maximize his profit? Aries houses Belfair houses Wexford houses (b) What is the maximum possible profit?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 33P: Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand...

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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.
The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.
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?
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?
It costs a pharmaceutical company 75,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for the drug is unknown, with the best case being 20,000 pounds, the most likely case 17,500 pounds, and the worst case 10,000 pounds. The drug sells for 125 per pound and leftover amounts of the drug can be sold for 30 per pound. To maximize annual expected profit, how many batches of the drug should the company produce? You can assume that it will produce the batches only once, before demand for the drug is known.
If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
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.
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?
If the number of competitors in Example 11.1 doubles, how does the optimal bid change?
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.
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?