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Yale University *
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MISC
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Industrial Engineering
Date
Nov 24, 2024
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doc
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Uploaded by ogwenogatamu
Interoffice Memorandum
FM:
M. L. Hatch, Ph.D., CEO Hatch Enterprises
TO:
Supervisor, Operations Research Team
RE:
Production Operations for Women’s Clothing Division
1.
We need to prepare our production schedule for the winter line in the Women’s Clothing
Division.
I wish to have your input before I meet with Ted Lawson, the production manager.
I
want you to determine the quantity of each clothing item to produce given our production
capacity and the raw materials we have available.
We need to accurately plan our production
schedule because what we produce will be in the stores by November.
We must pay our
designers $500,000 for their work on the line.
We also plan to have three fashion shows that
will cost $1,500,000 each.
2.
We have determined the price per unit of clothing and the cost to produce each unit of clothing.
This information, along with the materials requirements, is shown in the table below.
Clothing
Item
Materials
Requirements
Selling Price (per
unit)
Labor and Machine
Cost (per unit)
Wool Slacks
3 yards of wool
2 yards of acetate lining
$300
$160
Cashmere Sweater
1.5 yards of cashmere
450
150
Silk Blouse
1.5 yards of silk
180
100
Silk Camisole
0.5 yards of silk
120
60
Long Skirt
2 yards of rayon
270
120
Wool Blazer
2.5 yards of wool
1.5 yards of acetate lining
320
140
Velvet Pants
3 yards of velvet
350
175
Cotton Sweater
1.5 yards of cotton
130
60
Cotton Miniskirt
0.5 yards of cotton
75
40
Velvet Shirt
1.5 yards of velvet
200
160
Button-down Blouse
1.5 yards of rayon
120
90
I have 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 cotton for
production.
The price per yard of each type of material is shown in the table below.
Material
Price per yard
Material
Price per yard
Wool
$9.00
Acetate
$1.50
Cashmere
60.00
Silk
13.00
Rayon
2.25
Velvet
12.00
Cotton
2.50
3.
Any material that is not used can be sent back to the textile wholesaler for a full refund,
although scrap material cannot be sent back.
(This makes the materials costs a variable cost
rather than a fixed cost.)
Production of the cotton sweaters leaves leftover scrap material.
Specifically, 2 yards of material is used in production for each one but only 1.5 is needed and so
0.5 yard is left over.
We do not want to waste material, so whenever a cotton sweater is
produced, a cotton miniskirt will also be produced from the leftover.
4.
Some items have limited demand and we’ve asked the marketing department to provide us with
a forecast of potential sales.
Marketing has forecasted that we can sell 5,500 pairs of velvet
pants and 6,000 velvet shirts.
We do not want to produce over the forecast since these are
trendy items and we can not sell them if they go out of style.
The cashmere sweater is also
limited because of its high cost.
We should not produce any more than 4,000 cashmere
sweaters.
Marketing also believes we can sell at most 12,000 silk blouses and 15,000 silk
camisoles.
The maximum demand for wool slacks is believed to be 7,000 and for wool blazers
is 5,000.
I also feel that we should produce at least 2,800 long skirts and at least 4,000 button-
down blouses.
5.
Formulate the problem as a linear program to find a schedule that will maximize profits.
a)
Ted is trying to convince me not to produce the velvet shirts since demand has been low.
He
believes that the fixed production cost for this item alone is $500,000.
He feels that the net
contribution to profit of this item, even at the maximum demand can not cover the costs.
Given that we have already purchased our materials, what would you tell Ted?
b)
Which resources are the limiting factors?
What is our over all level of expected profit from
this schedule (including the design and fashion show costs)?
c)
The textile wholesaler has informed me that another customer has canceled his order.
We
can have 10,000 more yards of acetate.
Do we want it?
If not, why not and if so, what
should we pay for it?
d)
We can also purchase more silk and wool.
Is this a good idea?
How much of each can we
purchase without changing the optimal mix of items in the production schedule?
e)
Marketing has revised their forecast for the velvet pants to 6,500.
Should we produce more
pants with the same resources we have?
How does this change our profit?
6.
General Instructions;
I want your results in the form of a report by midnight on 5 December
2023.
I will create a drop box in GA View for you to load your files.
You may work in teams
of no more than 4 people on this project. Explain the problem that you are solving and provide
whatever background information you feel is necessary as an introduction to your report.
Assume that I know nothing about the field of Operations Research, include whatever additional
explanations you think might be helpful for me to understand and interpret your results.
Attach
the minimal amount
of excel reports, or tabular results to back up your recommendations.
Type
your report and provide clear explanations to all the questions.
Shoot for 3 - 5 pages (double
spaced) for the text of the paper.
Include a cover sheet and use margins of no larger than one
inch around the page.
You will also be graded on grammar and spelling.
If you have any
questions regarding this project, feel free to stop by FA 303 and ask questions.
Good Luck!
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