a) b) c) d) e) f) g) h) i) What is the optimal solution (in words? An additional 4 hours of shaper time became available. Evaluate the effect? Explain- Two hours of Grinder time was lost. Evaluate the effect? An additional 20 units of component 3 was requested. Evaluate the effect. The demand for component 2 decreased by 30 units. Evaluate the effect Suppose that the profit contribution of component 1 increases to $9.00. What is the new optimal solution? Suppose that the profit contribution of component 3 decrease by $2.00 . Would the optimal solution change Is the problem degenerate? Explain! Are there alternative optima in this problem? Explain

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter5: Network Models
Section: Chapter Questions
Problem 1C
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a) b) c) d) e) f) g) h) i) What is the optimal solution (in words? An additional 4 hours of shaper time became available. Evaluate the effect? Explain- Two hours of Grinder time was lost. Evaluate the effect? An additional 20 units of component 3 was requested. Evaluate the effect. The demand for component 2 decreased by 30 units. Evaluate the effect Suppose that the profit contribution of component 1 increases to $9.00. What is the new optimal solution? Suppose that the profit contribution of component 3 decrease by $2.00 . Would the optimal solution change Is the problem degenerate? Explain! Are there alternative optima in this problem? Explain
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
6.
4.
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.
C1 = units of component 1 manufactured
C2 = units of component 2 manufactured
C; = units of component 3 manufactured
Let
8C; +
6C, +
4C1
6C, +
4C,
5C2
Маx
9C3
4C; < 7200
2C; < 6600
C3 < 200
< 1000
< 1000
2 600
s.t.
+
+
C1
C2
C1
C; 20
Transcribed Image Text: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 6. 4. 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. C1 = units of component 1 manufactured C2 = units of component 2 manufactured C; = units of component 3 manufactured Let 8C; + 6C, + 4C1 6C, + 4C, 5C2 Маx 9C3 4C; < 7200 2C; < 6600 C3 < 200 < 1000 < 1000 2 600 s.t. + + C1 C2 C1 C; 20
Microsoft Excel 14.0 Answer Report
Report Created: 10/16/2015 2:52:09 AM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Objective Cell (Max)
Original Value Final Value
Name
SE$3 Profit
Variable Cells
Cell
10800
Cell
Name
Original Value
Final Value
Integer
$B$2 number of units c1
$C$2 number of units c2
$D$2 number of units c3
600 Contin
700 Contin
200 Contin
Constraints
Slack
Cell
ŞE$10 C1 minimum
Name
Cell Value
Formula
Status
600 ŞE$10>=$G$10 Binding
SE$5 Shaper
7200 ŞE$5<=$G$5
Binding
Not
ŞE$6
Grinder
6300 ŞE$6<=$G$6
Binding
300
SE$7 C3 maximum
200 ŞE$7<=$G$7
Binding
Not
SE$8 C1 maximum
600 $E$8<=$G$8
Binding
400
Not
SE$9 C2 maximum
700 ŞE$9<=$G$9
Binding
300
Microsoft Excel 14.0 Sensitivity Report
Worksheet: [Assignment 1 S1 2015-16 solutionB.xlsx]Q2 LP formulation MAX
Variable Cells
Final Reduced Objective Allowable
Allowable
Value
Coefficient Increase
Cell
$B$2 number of units c1
$¢$2 number of units c2
$D$2 number of units c3
Name
Cost
Decrease
600
8
1
1E+30
700
6
3 0.666666667
200
9.
1E+30
3
Constraints
Final Shadow
Constraint Allowable
Allowable
Cell
Name
Value
Price
R.H. Side
Increase
Decrease
$E$10 C1 minimum
600
-1
600
400 85.71428571
SE$5 Shaper
ŞE$6
7200
1.5
7200
240
2800
Grinder
6300
6600
1E+30
300
ŞE$7 C3 maximum
SE$8 C1 maximum
200
3
200
700
100
600
1000
1E+30
400
SE$9
C2 maximum
700
1000
1E+30
300
Transcribed Image Text:Microsoft Excel 14.0 Answer Report Report Created: 10/16/2015 2:52:09 AM Result: Solver found a solution. All Constraints and optimality conditions are satisfied. Objective Cell (Max) Original Value Final Value Name SE$3 Profit Variable Cells Cell 10800 Cell Name Original Value Final Value Integer $B$2 number of units c1 $C$2 number of units c2 $D$2 number of units c3 600 Contin 700 Contin 200 Contin Constraints Slack Cell ŞE$10 C1 minimum Name Cell Value Formula Status 600 ŞE$10>=$G$10 Binding SE$5 Shaper 7200 ŞE$5<=$G$5 Binding Not ŞE$6 Grinder 6300 ŞE$6<=$G$6 Binding 300 SE$7 C3 maximum 200 ŞE$7<=$G$7 Binding Not SE$8 C1 maximum 600 $E$8<=$G$8 Binding 400 Not SE$9 C2 maximum 700 ŞE$9<=$G$9 Binding 300 Microsoft Excel 14.0 Sensitivity Report Worksheet: [Assignment 1 S1 2015-16 solutionB.xlsx]Q2 LP formulation MAX Variable Cells Final Reduced Objective Allowable Allowable Value Coefficient Increase Cell $B$2 number of units c1 $¢$2 number of units c2 $D$2 number of units c3 Name Cost Decrease 600 8 1 1E+30 700 6 3 0.666666667 200 9. 1E+30 3 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $E$10 C1 minimum 600 -1 600 400 85.71428571 SE$5 Shaper ŞE$6 7200 1.5 7200 240 2800 Grinder 6300 6600 1E+30 300 ŞE$7 C3 maximum SE$8 C1 maximum 200 3 200 700 100 600 1000 1E+30 400 SE$9 C2 maximum 700 1000 1E+30 300
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