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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
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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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.
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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