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?

Machine Hours
1.5
3
< 200
3.8333
per Item
=
MIN NUMBER OF 1
> 25
CHAIRS
Solution->
100
16.6667
2116.
667
RANGING TABLE
Original
Val
Variable
Value
Reduced
Lower
Upper
Bound
Cost
Bound
LOUNGE CHAIRS
100
|17
12.5
20.83
SMALL SOFA
16.67
25
20.4
34
Original
Val
Constraint
Dual
Slack/
Lower
Upper
Bound
Value
Surplus
Bound
FRAMING LABOR per
50
500
450
Infinity
item
CUTTING LABOR per
item
300
4.5
225
320
Yards of Material per
25
850
825
Infinity
Item
Machine Hours per Item 3.83
200
180
211.11
MIN NUMBER OF
75
25
100
CHAIRS
Transcribed Image Text:Machine Hours 1.5 3 < 200 3.8333 per Item = MIN NUMBER OF 1 > 25 CHAIRS Solution-> 100 16.6667 2116. 667 RANGING TABLE Original Val Variable Value Reduced Lower Upper Bound Cost Bound LOUNGE CHAIRS 100 |17 12.5 20.83 SMALL SOFA 16.67 25 20.4 34 Original Val Constraint Dual Slack/ Lower Upper Bound Value Surplus Bound FRAMING LABOR per 50 500 450 Infinity item CUTTING LABOR per item 300 4.5 225 320 Yards of Material per 25 850 825 Infinity Item Machine Hours per Item 3.83 200 180 211.11 MIN NUMBER OF 75 25 100 CHAIRS
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
SMALL
RHS Equation form
CHAIRS
SOFA
Maximize
Max 17LOUNGE CHAIRS +
25SMALL SOFA
17
25
FRAMING LABOR 3.5
6
< 500
3.5LOUNGE CHAIRS + 6SMALL
SOFA <= 500
per item
CUTTING LABOR 2.5
per item
3
< 300
2.5LOUNGE CHAIRS + 3SMALL
SOFA <= 300
Yards of Material 6.5
10.5
< 850
6.5LOUNGE CHAIRS +
per Item
10.5SMALL SOFA <= 850
=
< 200
Machine Hours
per Item
MIN NUMBER OF 1
1.5
3
1.5LOUNGE CHAIRS + 3SMALL
SOFA <= 200
%3D
> 25
LOUNGE CHAIRS >= 25
CHAIRS
OPTIMAL SOLUTION
LOUNGE
SMALL
RHS Dual
CHAIRS
SOFA
Maximize
17
25
FRAMING LABOR 3.5
< 500
per item
CUTTING LABOR 2.5
per item
Yards of Material
per Item
3
< 300
4.5
6.5
10.5
< 850
Lightshot Screenshot
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 SMALL RHS Equation form CHAIRS SOFA Maximize Max 17LOUNGE CHAIRS + 25SMALL SOFA 17 25 FRAMING LABOR 3.5 6 < 500 3.5LOUNGE CHAIRS + 6SMALL SOFA <= 500 per item CUTTING LABOR 2.5 per item 3 < 300 2.5LOUNGE CHAIRS + 3SMALL SOFA <= 300 Yards of Material 6.5 10.5 < 850 6.5LOUNGE CHAIRS + per Item 10.5SMALL SOFA <= 850 = < 200 Machine Hours per Item MIN NUMBER OF 1 1.5 3 1.5LOUNGE CHAIRS + 3SMALL SOFA <= 200 %3D > 25 LOUNGE CHAIRS >= 25 CHAIRS OPTIMAL SOLUTION LOUNGE SMALL RHS Dual CHAIRS SOFA Maximize 17 25 FRAMING LABOR 3.5 < 500 per item CUTTING LABOR 2.5 per item Yards of Material per Item 3 < 300 4.5 6.5 10.5 < 850 Lightshot Screenshot
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