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The NY Fashion Company
From the tenth floor of her office building, Diana Ricks watches her swarms of New Yorkers watching stores along streets. On this hot July day, she pays particular attention to the fashions worn by the various women and wonders what they will choose to wear in the fall. Her thoughts are not simply random thoughts; they are rooted of her work since she owns and manages the NY Fashion Company, a leader of women’s clothing company.
She usually meets her production manger, Ted Wallace, during this month 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. Diana relies upon the sales department forecasts because the items produced next month will appear in stores during September. Women generally buy the majority of the fall fashions when the clothing items first appear in department stores.
She turns back to her desk and looks at the clothing patterns designed almost six months ago, papers listing the of materials requirements for each pattern, and the demand forecasts for each pattern. She remembers the hectic and sometimes terrifying 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 $500,000 for their work on her fall line. With the cost of hiring runway models and the renting the conference hall, each of the three fashions show costs her an additional of $500,000. She also paid the following overhead costs on her fall line.
Material Handling $280,000
Production Planning Dept. $260,000
Set-up Indirect Cost $260,000
Shipping Department $200,000
Total $1,000,000
Her fall line consists of both professional and casual fashions. She has determined the prices for each clothing item by taking into account the item and the prestige of her company’s brand name.
The fall professional fashions include tailored wool slack, silk blouse, silk camisole, tailored skirt, and wool blazer. Price, material requirements, labor hours, and machine hours are shown in Table 1. The fall casual fashions include velvet pants, cotton sweater, cotton miniskirt, velvet shirt and button-down blouse. The other pertinent information regarding price, material requirements, labor hours and machine hours are shown in Table 2.
Table 1. Professional clothing items with price, labor hours, and machine hours requirements.
Clothing
Items Price Materials Requirements Labor hrs @$20/hr Machine hrs @$10/hr
Tailored wool slacks $300 3 yard of wool
2 yards of acetate for lining 5 6
Silk blouse $180 1.5 yards of silk 3 4
Silk camisole $120 0.5 yard of silk 2 2
Tailored skirt $270 2 yards of rayon
1.5 yards of acetate for lining 4 4
Wool blazer $320 2.5 yards of wool
1.5 yards of acetate for lining 5 4
Table 2. Causal clothing items with price, labor hours, and machine hours requirements.
Clothing Item Price Materials Requirements Labor hrs @$20/hr Machine hrs @$10/hr
Velvet pants $350 3 yard of velvet
2 yards of acetate for lining 5 7.5
Cotton sweater $130 1.5 yards of cotton 2 2
Cotton miniskirt $75 0.5 yard of cotton 1 2
Velvet shirt $200 1.5 yards of velvet 5 6
Button-down blouse $120 1.5 yards of rayon 3 3
Ted has told Diana that he ordered 45,000 yards of wool, 28,000 yards of acetate, 18,000 yards of silk, 30,000 yards of rayon, 20,000 yards of velvet, and 30,000 yards of cotton for production. The prices of the materials are listed in Table 3.
Table 3. Cost of materials
Materials Cost per yard, $
Wool 9.00
Acetate 1.5
Silk 13.00
Rayon 2.25
Velvet 12.00
Cotton 2.5
Any material that is not used in production can be sent back to the textile wholesaler for full refund, although scrap material cannot be sent back to the wholesaler.
Ted also informs her that the production of both silk blouse and cotton sweater produces 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. In order not to waste the material, she told Ted to use the rectangular scrap of silk or cotton to produce a silk camisole or cotton miniskirt, respectively. It means that whenever a silk blouse is produced, a silk camisole 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, sales department has forecasted that it can sell only 5,500 pairs of velvet pants and 6,000 velvet shirts. However, the company can produce less than the forecasted demand, since the company is not required to meet the demand. The silk blouses and camisoles have also limited demand because many women think silk is too hard to care for, and sales department projects that it can sell at most 12,000 silk blouses and 15,000 silk camisoles.
General hint: Make necessary assumption(s) if it is required to do a complete analysis.
a. Formulate and solve a linear programming problem to maximize total contribution margins given the production, resource, and demand constraints.
Hint: Compute unit contribution margin for each of the products as contribution margin = Sale price – direct costs. The calculated unit contribution will be used for the coefficient of the decision variables of your LP model. Interpret your computer results. The production plan that you obtain from the computer solution will be used for parts c through f.
b. The textile wholesaler informs Diana that since another textile customer canceled his order, she can be obtained an extra 10,000 yard of acetate. How many of each clothing item the company should now produce to maximize profit?
Hint: This is a sensitivity analysis. Make sure the acetate is a binding resource; otherwise the sensitivity analysis is not required.
c. Determine income statement (as of the end of Fall) based on the production plan developed in part a. Assume all clothing items planned in part (a) can be sold in the market. If a clothing item is not selected (determined by the LP model), it means it will not be produced.
d. Calculate the unit profit for each of the clothing items using the traditional volume-based costing method. Use the optimal production plan developed in part (a) and the following basis for allocating overhead costs.
Indirect cost Allocation Basis
Designer cost Direct material
Fashion show costs Direct labor hours
Material Handling Direct material
Production Planning Dept. Direct labor hours
Set-up Indirect Cost Direct labor hours
Shipping Department Direct material
Note: assumptions might be required for each part as long as they are made realistically. Depending on what you assume, solutions will be different from one person to another. For example, if the optimal solution for any of the clothing items is equal to 2 units, you may impose a constraint to drop it from your solution mix.
