1 2 3 4 5 6 7 S 9 12 13 begin on a new line of fashions, but April still has a significant supply of fabric for last year's line. They would like to use up what they can, but have allocated only one week of production time before the changeover to the new designs. They have chosen to focus on at most 4 products: pants, skirts, vests and caps. Each item requires denim, cutting sewing and packaging. 14 15 16 17 April formulated the problem as a linear program and used Solver to obtain the solution and sensitivity report below: B D E F G HIJ N 0 P к L M Microsoft Excel 12.0 Sensitivity Report Worksheet: [1205-SA6-08F.xlsx]A6-#1 Report Created: 10/30/2008 5:37:55 PM Adjustable Cells A6-#1 April Fashion Manufacturing Demin (sqm) 1 Cutting (min) 3 Sewing (min) 7 10 Packaging (min) 1 11 Pants Skirts Vests P S V #made 350 profit S 3 Constraints 850 2 0.6 23 1 0 2 0.7 3 6 1 Caps C 0 1 0.3 2 3 1 Total 2750 860 S 2750 S 5000 S 1200 S 1000 3000 5000 1200 Cell Name $B$4 #made P SCS4 #made S SDS4 SES4 Constraints # made V #made C Final Reduced Objecti Allowab Allowable Value Cost Coeffic Increas Decrease 3 1.6667 2 2 1 350 850 0 0 0 0 -0.75 -1 1 1 0.71429 0.75 1E+30 1 1E+30 Final Shadow Constr: Allowab Allowable Cell Name Value Price R.H. Si Increas Decrease SFS7 Demin (sqm) 860 0 1000 1E+30 140 SFSS Cutting (min) 2750 0 3000 1E+30 250 SFS9 Sewing (min) 5000 0.25 5000 1000 1400 SFS10 Packaging (m 1200 1.25 1200 200 485.714 a) How many of each product should be made? b) Suppose that 100 square meters of denim is found to be damaged and cannot be used. What is the impact on total profits? c) Suppose employees on the packaging line are willing to work overtime. The added cost will be $22 per hour. Should you accept their offer? Explain why or why not. If you use the overtime, how much should you use?
1 2 3 4 5 6 7 S 9 12 13 begin on a new line of fashions, but April still has a significant supply of fabric for last year's line. They would like to use up what they can, but have allocated only one week of production time before the changeover to the new designs. They have chosen to focus on at most 4 products: pants, skirts, vests and caps. Each item requires denim, cutting sewing and packaging. 14 15 16 17 April formulated the problem as a linear program and used Solver to obtain the solution and sensitivity report below: B D E F G HIJ N 0 P к L M Microsoft Excel 12.0 Sensitivity Report Worksheet: [1205-SA6-08F.xlsx]A6-#1 Report Created: 10/30/2008 5:37:55 PM Adjustable Cells A6-#1 April Fashion Manufacturing Demin (sqm) 1 Cutting (min) 3 Sewing (min) 7 10 Packaging (min) 1 11 Pants Skirts Vests P S V #made 350 profit S 3 Constraints 850 2 0.6 23 1 0 2 0.7 3 6 1 Caps C 0 1 0.3 2 3 1 Total 2750 860 S 2750 S 5000 S 1200 S 1000 3000 5000 1200 Cell Name $B$4 #made P SCS4 #made S SDS4 SES4 Constraints # made V #made C Final Reduced Objecti Allowab Allowable Value Cost Coeffic Increas Decrease 3 1.6667 2 2 1 350 850 0 0 0 0 -0.75 -1 1 1 0.71429 0.75 1E+30 1 1E+30 Final Shadow Constr: Allowab Allowable Cell Name Value Price R.H. Si Increas Decrease SFS7 Demin (sqm) 860 0 1000 1E+30 140 SFSS Cutting (min) 2750 0 3000 1E+30 250 SFS9 Sewing (min) 5000 0.25 5000 1000 1400 SFS10 Packaging (m 1200 1.25 1200 200 485.714 a) How many of each product should be made? b) Suppose that 100 square meters of denim is found to be damaged and cannot be used. What is the impact on total profits? c) Suppose employees on the packaging line are willing to work overtime. The added cost will be $22 per hour. Should you accept their offer? Explain why or why not. If you use the overtime, how much should you use?
Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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Transcribed Image Text:1. April Fashions manufactures denim children's clothing for sale through independent retailers. Production will soon
begin on a new line of fashions, but April still has a significant supply of fabric for last year's line. They would like
to use up what they can, but have allocated only one week of production time before the changeover to the new designs.
They have chosen to focus on at most 4 products: pants, skirts, vests and caps. Each item requires denim, cutting,
sewing and packaging.
1
2
3
4
5
6
7
8
9
12
13
14
Demin (sqm)
Cutting (min)
Sewing (min)
10 Packaging (min)
11
HEE
April formulated the problem as a linear program and used Solver to obtain the solution and sensitivity report below:
B C D
G H I | J | K
M
E
F
0
P
Microsoft Excel 12.0 Sensitivity Report
Worksheet: [1205-SA6-08F.xlsx)A6-#1
Report Created: 10/30/2008 5:37:55 PM
Adjustable Cells
15
16
17
A6-#1 April Fashion Manufacturing
#made 350 850
3
2
profit S
Constraints
Pants Skirts Vests
P S
V
1
3
7
1
6231
0.6
0
NO
2
0.7
331
6
1
Caps
с
0
1
0.3
-ENW
2
3
1
Total
2750
860 S
2750 S
5000 S
1200 S
1000
3000
5000
1200
Cell Name
SBS4
#made P
SCS4 #made S
SDS4
#made V
SES4
#made C
Constraints
Final Reduced Objecti Allowab Allowable
Value
Cost Coeffic Increas Decrease
3 1.6667
1
2
1 0.71429
1E+30
1E+30
350
850
0
0
0
0
-0.75
-1
2
1
0.75
1
Cell
Name
Demin (sqm)
SFS7
SFSS Cutting (min)
Final Shadow Constr: Allowab Allowable
Value Price R.H. Si Increas Decrease
860 0 1000 1E+30 140
2750 0 3000 1E-30 250
5000 0.25 5000 1000
SFS9 Sewing (min)
1400
SFS10 Packaging (m 1200 1.25 1200 200 485.714
a) How many of each product should be made?
b)
Suppose that 100 square meters of denim is found to be damaged and cannot be used. What is the impact on
total profits?
c) Suppose employees on the packaging line are willing to work overtime. The added cost will be $22 per hour.
Should you accept their offer? Explain why or why not. If you use the overtime, how much should you use?
d) The skirts have met with unexpectedly high interest and it has been possible to increase the price such that the
profit is now $2.50 per skirt. Should the quantities of the various products change? Explain.
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