question: How much profit is added if you are given an additional 50 Yards of Material?
question: How much profit is added if you are given an additional 50 Yards of Material?
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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Question
question:
How much profit is added if you are given an additional 50 Yards of Material?
![A company produces Lounge Chairs and Small Sofas. It uses Two Labor Types (Framing and
Cutting time per item in hours), Material and a Machine in the manufacturing process.
Management has put a minimum on the number (25) of Lounge Chairs which must be
produced. The profit per Lounge Chair is $17.00 and per Small Sofa is $25.00. Below are the
LP formulation and the QM results tables.
PROBLEM STATEMENT
LOUNGE
CHAIRS
RHS Equation form
SMALL
SOFA
Maximize
17
25
Max 17LOUNGE CHAIRS +
25SMALL SOFA
FRAMING LABOR 3.5
6
< 500
3.5LOUNGE CHAIRS + 6SMALL
per item
SOFA <= 500
CUTTING LABOR 2.5
per item
Yards of Material 6.5
per Item
< 300
2.5LOUNGE CHAIRS + 3SMALL
SOFA <= 300
10.5
< 850
6.5LOUNGE CHAIRS +
10.5SMALL SOFA <= 850
< 200
Machine Hours
per Item
1.5
3
1.5LOUNGE CHAIRS + 3SMALL
SOFA <= 200
MIN NUMBER OF 1
CHAIRS
> 25
LOUNGE CHAIRS >= 25
OPTIMAL SOLUTION
LOUNGE
SMALL
RHS
Dual
CHAIRS
SOFA
Maximize
17
25
FRAMING LABOR 3.5
6
< 500 0
per item
CUTTING LABOR 2.5
per item
3
< 300
4.5
Yards of Material
6.5
10.5
< 850
per Item
Lightshot Screenshot
3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec2937f9-36f2-4f7d-ab0a-c8e482869dab%2F76d48278-0013-4a8c-8f71-fd7ac3c269da%2Fxktmx4r_processed.png&w=3840&q=75)
Transcribed Image Text:A company produces Lounge Chairs and Small Sofas. It uses Two Labor Types (Framing and
Cutting time per item in hours), Material and a Machine in the manufacturing process.
Management has put a minimum on the number (25) of Lounge Chairs which must be
produced. The profit per Lounge Chair is $17.00 and per Small Sofa is $25.00. Below are the
LP formulation and the QM results tables.
PROBLEM STATEMENT
LOUNGE
CHAIRS
RHS Equation form
SMALL
SOFA
Maximize
17
25
Max 17LOUNGE CHAIRS +
25SMALL SOFA
FRAMING LABOR 3.5
6
< 500
3.5LOUNGE CHAIRS + 6SMALL
per item
SOFA <= 500
CUTTING LABOR 2.5
per item
Yards of Material 6.5
per Item
< 300
2.5LOUNGE CHAIRS + 3SMALL
SOFA <= 300
10.5
< 850
6.5LOUNGE CHAIRS +
10.5SMALL SOFA <= 850
< 200
Machine Hours
per Item
1.5
3
1.5LOUNGE CHAIRS + 3SMALL
SOFA <= 200
MIN NUMBER OF 1
CHAIRS
> 25
LOUNGE CHAIRS >= 25
OPTIMAL SOLUTION
LOUNGE
SMALL
RHS
Dual
CHAIRS
SOFA
Maximize
17
25
FRAMING LABOR 3.5
6
< 500 0
per item
CUTTING LABOR 2.5
per item
3
< 300
4.5
Yards of Material
6.5
10.5
< 850
per Item
Lightshot Screenshot
3.
![Machine Hours
1.5
< 200
3.8333
per Item
MIN NUMBER OF 1
> 25
CHAIRS
Solution->
100
16.6667
2116.
667
RANGING TABLE
Variable
Value
Reduced
Original
Val
Lower
Bound
Upper
Bound
Cost
LOUNGE CHAIRS
100
17
12.5
20.83
SMALL SOFA
| 16.67
25
20.4
| 34
Slack/
Surplus
Constraint
Dual
Value
Original
Val
Lower
Upper
Bound
Bound
FRAMING LABOR per
50
500
450
Infinity
item
320
CUTTING LABOR per
item
4.5
300
225
Yards of Material per
Item
25
850
825
Infinity
Machine Hours per Item 3.83
200
180
211.11
MIN NUMBER OF
75
25
100
CHAIRS
3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec2937f9-36f2-4f7d-ab0a-c8e482869dab%2F76d48278-0013-4a8c-8f71-fd7ac3c269da%2Fzyvxcc_processed.png&w=3840&q=75)
Transcribed Image Text:Machine Hours
1.5
< 200
3.8333
per Item
MIN NUMBER OF 1
> 25
CHAIRS
Solution->
100
16.6667
2116.
667
RANGING TABLE
Variable
Value
Reduced
Original
Val
Lower
Bound
Upper
Bound
Cost
LOUNGE CHAIRS
100
17
12.5
20.83
SMALL SOFA
| 16.67
25
20.4
| 34
Slack/
Surplus
Constraint
Dual
Value
Original
Val
Lower
Upper
Bound
Bound
FRAMING LABOR per
50
500
450
Infinity
item
320
CUTTING LABOR per
item
4.5
300
225
Yards of Material per
Item
25
850
825
Infinity
Machine Hours per Item 3.83
200
180
211.11
MIN NUMBER OF
75
25
100
CHAIRS
3.
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