Case $3-3$ 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 vel$-$

vet, and $30,000$ yards of cotton for production. The prices of the

materials are listed below. Any material that is not used in production can be sent back

to the textile wholesaler for a full refund, although scrap mate$-$

rial cannot be sent back to the wholesaler.

She knows that the production of both the silk blouse and cot$-$

ton 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,

$1\mathrm{.}5$ yards are used for the silk blouse or the cotton sweater and

$0\mathrm{.}5$ yard is left as scrap material. She does not want to waste the

material, so she plans to use the rectangular scrap of silk or cot$-$

ton 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 lim$-$

ited 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

demand because once the pants and shirts go out of style, thecompany cannot sell them. TrendLines can produce less than the

forecasted demand, however, since the company is not required

to meet the demand. The cashmere sweater also has limited

demand because it is quite expensive, and TrendLines knows it

can sell at most $4,000$ cashmere sweaters. The silk blouses and

camisoles have limited 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 slacks,

tailored skirts, and wool 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 blazers. Katherine wants to meet at least $60$ percent of the

demand for these two items to maintain her loyal customer base

and not lose business in the future. Although the demand for

t

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 atten$-$

tion 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 musings; they are critical to her work since she 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. Accurate 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 pattern, 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 her fall line.

With the cost of hiring runway models, hair stylists, and make$-$up

artists; sewing and fitting clothes; building the set; choreograph$-$

ing 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 item, and the prestige of the TrendLines brand name.