Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Question 2
CWD Manufacturing makes three components for sale to refrigeration companies. The
components are processed on two machines: a shaper and a grinder. The times (in minutes)
required on each machine are as follows:
Machine
| Component | Shaper | Grinder |
| 1 | 6 | 4 |
| 2 | 4 | 5 |
| 3 | 4 | 2 |
The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than
200 units of component 3 can be sold, but up to 1000 units of each of the other components can
be sold. In fact, the company already has orders for 600 units of component 1 that must be
satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively.
(see image)
If there are two possible answers one will suffice. Where necessary a range analysis must be shown.(convert to minutes)
a) What is the optimal solution (in words)?
b) An additional 4 hours of shaper time became available. Evaluate the effect? Explain
c) Two hours of Grinder time was lost. Evaluate the effect?
d) An additional 20 units of component 3 was requested. Evaluate the effect
e) The demand for component 2 decreased by 30 units. Evaluate the effect
f) Suppose that the profit contribution of component 1 increases to $9.00.
What is the new optimal solution?
g) Suppose that the profit contribution of component 3 decrease by $2.00 . Would the optimal solution change
h) Is the problem degenerate? Explain!
i) Are there alternative optima in this problem? Explain
Transcribed Image Text:Microsoft Excel 14.0 Answer Report
Report Created: 10/16/201525209 AM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Objective Cell (Max)
Final Value
Cell
Name
Original Value
SESI
Profit
10800
Variable Cells
Final Value
Cell
Name
Original Value
Integer
SBS2
SCS2
number of units ci
600 Contin
number of units c2
700 Contin
SDS2
number of units 3
200 Contin
Constraints
Cell
Name
Cell Value
Formula
satus
Slack
600 SE$10-SG$10 Binding
Binding
ŞE$10 Ci minimum
SESS
Shaper
7200 SESS-SGSS
Not
SESE
Grinder
6300 SES6e-SG56
Binding
300
SEST
C3 maimum
200 SEST-SGS7
Binding
Not
SESE
Ci maximum
600 SESB-SGS8
Binding
Not
Binding
400
SES9 C2 maximum
700 SES9-SG59
300
Microsoft Excel 14.0 Sensitivity Report
Worksheet: JAssignment 1 S1 2015-16 solutions.xxQ2 LP formulation MAX
Variable Cells
Final Reduced Objective Allowable Allowable
Cell
Name
Value
Cost
Coefficient
Increase
Decrease
SB$2 number of units ci
600
1E-30
1
3 0.666666667
SCS2
number of units 2
700
SD$2
number of units c3
200
1E+30
Constraints
Final
Shadow
Constraint Alowable
Allowable
Cell
Name
Value
Price
RH. Side
Increase
Decrease
400 85.71428571
SE$10 C1 minimum
SESS
600
-1
600
Shaper
7200
1.5
7200
240
2800
SES6
Grinder
6300
6600
1E30
300
C3 maximum
C1 maximum
SEST
200
200
700
100
SESE
600
1000
1E30
400
SESS
C2 maximum
700
1000
1E+30
300
Transcribed Image Text:Let C = units of component 1 manufactured
C, = units of component 2 manufactured
C; = units of component 3 manufactured
8C; +
6C; +
4C; +
Маx
6C, +
4C, +
5C, +
9C;
4C; s 7200
2C; s 6600
C; s 200
s 1000
S 1000
2 600
C1, C2, C; 20
s.t.
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