question:  What is the amount of increase in profit for each Machine Hour added and what is the maximum number of yards that can be added for this amount of profit increase?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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What is the amount of increase in profit for each Machine Hour added and what is the maximum number of yards that can be added for this amount of profit increase?

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.
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.
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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