Fabrics and Fall Fashions From the 10 th floor of her office building, Katherine Rally watches the swarms of New Yorkers fight their way through the streets infested with yellow cabs and the sidewalks littered with hot dog stands. On this sweltering July day, she pays particular attention to the fashions worn by the various women and won: ders what they will choose to wear in the fall. Her thoughts are not simply random musings; they are critical to her work since the owns and manages TrendLines, an elite women's clothing company. Today is an especially important day because she must meet with Ted Lawson, the production manager, to decide upon next month's production plan for the fall line. Specifically, she must determine the quantity of each clothing item she should produce given the plant's production capacity, limited resources, and demand forecasts. Aceurate planning for next month's production is critical to fall sales since the items produced next month will appear in stores during September and women generally buy the majority of the fall fashions when they first appear in September. She turns back to her sprawling glass desk and looks at the numerous papers covering it. Her eyes roam across the clothing. patterns designed almost six months ago, the lists of material requirements for each pattem, and the lists of demand forecasts for each pattern determined by customer surveys at fashion shows. She remembers the hectic and sometimes nightmarish days of designing the fall line and presenting it at fashion shows in New York, Milan, and Paris. Ultimately, she paid her team of six designers a total of $860,000 for their work on ber fall line, With the cost of hiring runway models, hair stylists, and make-up artists; sewing and fitting clothes; building the set; choreographing and rehearsing the show; and renting the conference hall, each of the three fashion shows cost her an additional $2,700,000. She studies the clothing patterns and material requirements. Her fall line consists of both professional and casual fashions. She determined the price for each clothing item by taking into account the quality and cost of material, the cost of labor and machining, the demand for the itern, and the prestige of the TrendLines brand name. The fall professional fashions include. Case 33 Fobria and Fall Fations 117 Any material that is not used in production cin be sent back to the textile wholesaler for a full refund, although serap material cannot be sent back to the wholesaler. She knows that the production of both the silk blouse and cotton sweater leaves leftover scraps of material. Specifically, for the production of one silk blouse or one cotton sweater, 2 yards of silk and cotton, respectively, are needed. From these 2 yards, 1.5 yards are used for the silk blouse or the cotton sweater and 0.5 yard is left as scrap material. She does not want fo waste the material, so she plans to use the rectangular scrap of silk or cotton to produce a silk camisole or cotton miniskirt, respectively. Therefore, whenever a silk blouse is produced, a silk camisole is also produced. Likewise, whenever a cotton sweater is produced, a cotton miniskirt is also produced. Note that it is possible to produce a silk camisole without producing a silk blouse and a cotton miniskirt without producing a cotton sweater. The demand forecasts indicate that some items have limited demand. Specifically, because the velvet pants and velvet shirts are fashion fads, TrendLines has forecasted that it can sell only 5,500 pairs of velvet pants and 6,000 velvet shirts. TrendLines does not want to produce more than the forecasted The fall casual fashions include: She knows that for the next month, she has ordered 45,000 yards of wool, 28,000 yards of acetate, 9,000 yards of cashmere, 18,000 yards of silk, 30,000 yards of rayon, 20,000 yards of velvet, and 30,000 yards of colton for production. The prices of the materials are listed below. demand because once the pants and shirts go out of style, the company cannot sell them. TrendLines can produce less than the forecasted demand, however, since the eompany is not required - to meet the demand. The cashmere sweater also has limited demand because it is quite expensive, and Trendt ines knows it can sell at most 4,000 cashmere sweaters. The silk blouses and camisoles have timited demand because many women think silk is too hard to care for, and TrendLines projects that it can sell at most 12,000 silk blouses and 15,000 silk camisoles. The demand forecasts also indicate that the wool stacks, tailored skirts, and woot blazers have a great demand because they are basic items needed in every professional wardrobe, Specifically, the demand is 7,000 pairs of wool slacks and 5,000 wool blizers. Katherine wants to meet at least 60 percent of the demand for these two itens to maintain her loyal customer base and not lose business in the future. Although the demand for tailored skirts could not be estimated, Katherine feels she should make at least 2,800 of them. a. Ted is trying to convince Katherine not to produce any velvet shirts since the demand for this fashion fad is quite low. He argues that this fashion fad alone accounts for $500,000 of the fixed design and other costs. The net contribution (price of clothing item - materials cost - labor cost) from selling the fashion fad should cover these fixed costs. Each velvet shirt generates a net contribution of $22. He argues that given the net contribution, even satisfying the maximum demand will not yield a profit. What do you think of Ted's argument? b. Formulate and solve a linear programming problem to maximize profit given the production, resource, and demand constraints. Fabrics and Fall Fashions From the 10 th floor of her office building, Katherine Rally watches the swarms of New Yorkers fight their way through the streets infested with yellow cabs and the sidewalks littered with hot dog stands. On this sweltering July day, she pays particular attention to the fashions worn by the various women and won: ders what they will choose to wear in the fall. Her thoughts are not simply random musings; they are critical to her work since the owns and manages TrendLines, an elite women's clothing company. Today is an especially important day because she must meet with Ted Lawson, the production manager, to decide upon next month's production plan for the fall line. Specifically, she must determine the quantity of each clothing item she should produce given the plant's production capacity, limited resources, and demand forecasts. Aceurate planning for next month's production is critical to fall sales since the items produced next month will appear in stores during September and women generally buy the majority of the fall fashions when they first appear in September. She turns back to her sprawling glass desk and looks at the numerous papers covering it. Her eyes roam across the clothing. patterns designed almost six months ago, the lists of material requirements for each pattem, and the lists of demand forecasts for each pattern determined by customer surveys at fashion shows. She remembers the hectic and sometimes nightmarish days of designing the fall line and presenting it at fashion shows in New York, Milan, and Paris. Ultimately, she paid her team of six designers a total of $860,000 for their work on ber fall line, With the cost of hiring runway models, hair stylists, and make-up artists; sewing and fitting clothes; building the set; choreographing and rehearsing the show; and renting the conference hall, each of the three fashion shows cost her an additional $2,700,000. She studies the clothing patterns and material requirements. Her fall line consists of both professional and casual fashions. She determined the price for each clothing item by taking into account the quality and cost of material, the cost of labor and machining, the demand for the itern, and the prestige of the TrendLines brand name. The fall professional fashions include. Case 33 Fobria and Fall Fations 117 Any material that is not used in production cin be sent back to the textile wholesaler for a full refund, although serap material cannot be sent back to the wholesaler. She knows that the production of both the silk blouse and cotton sweater leaves leftover scraps of material. Specifically, for the production of one silk blouse or one cotton sweater, 2 yards of silk and cotton, respectively, are needed. From these 2 yards, 1.5 yards are used for the silk blouse or the cotton sweater and 0.5 yard is left as scrap material. She does not want fo waste the material, so she plans to use the rectangular scrap of silk or cotton to produce a silk camisole or cotton miniskirt, respectively. Therefore, whenever a silk blouse is produced, a silk camisole is also produced. Likewise, whenever a cotton sweater is produced, a cotton miniskirt is also produced. Note that it is possible to produce a silk camisole without producing a silk blouse and a cotton miniskirt without producing a cotton sweater. The demand forecasts indicate that some items have limited demand. Specifically, because the velvet pants and velvet shirts are fashion fads, TrendLines has forecasted that it can sell only 5,500 pairs of velvet pants and 6,000 velvet shirts. TrendLines does not want to produce more than the forecasted The fall casual fashions include: She knows that for the next month, she has ordered 45,000 yards of wool, 28,000 yards of acetate, 9,000 yards of cashmere, 18,000 yards of silk, 30,000 yards of rayon, 20,000 yards of velvet, and 30,000 yards of colton for production. The prices of the materials are listed below. demand because once the pants and shirts go out of style, the company cannot sell them. TrendLines can produce less than the forecasted demand, however, since the eompany is not required - to meet the demand. The cashmere sweater also has limited demand because it is quite expensive, and Trendt ines knows it can sell at most 4,000 cashmere sweaters. The silk blouses and camisoles have timited demand because many women think silk is too hard to care for, and TrendLines projects that it can sell at most 12,000 silk blouses and 15,000 silk camisoles. The demand forecasts also indicate that the wool stacks, tailored skirts, and woot blazers have a great demand because they are basic items needed in every professional wardrobe, Specifically, the demand is 7,000 pairs of wool slacks and 5,000 wool blizers. Katherine wants to meet at least 60 percent of the demand for these two itens to maintain her loyal customer base and not lose business in the future. Although the demand for tailored skirts could not be estimated, Katherine feels she should make at least 2,800 of them. a. Ted is trying to convince Katherine not to produce any velvet shirts since the demand for this fashion fad is quite low. He argues that this fashion fad alone accounts for $500,000 of the fixed design and other costs. The net contribution (price of clothing item - materials cost - labor cost) from selling the fashion fad should cover these fixed costs. Each velvet shirt generates a net contribution of $22. He argues that given the net contribution, even satisfying the maximum demand will not yield a profit. What do you think of Ted's argument? b. Formulate and solve a linear programming problem to maximize profit given the production, resource, and demand constraints