,Appendix A - Linear Programming Using the Excel Solver
APPENDIX A
LINEAR PROGRAMMING USING THE EXCEL SOLVER
1. Excel Solution
X Y Total
Decision 6 0
Profit $3 $1 $18
Resources
X Y Used Capacity
A 12 14 72 <= 85
B 3 2 18 <= 18
C 1 0 <= 4
Graphical solution--the problem requested the Excel solution, but the following graphical
solution is provided for classroom use if desired.
A-1
© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
,Appendix A - Linear Programming Using the Excel Solver
2.
A B Total
Decision 15 10
Cost $2 $4 $70
Resources
A B Used Capacity
A 4 6 120 >= 120
B 2 6 90 >= 72
C 1 10 >= 10
Graphical solution--the problem requested the Excel solution, but the following graphical
solution is provided for classroom use if desired.
A-2
© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
, Appendix A - Linear Programming Using the Excel Solver
3. a. Maximize Z = 20X1 + 6X2 + 8X3
s.t. 8X1 + 2X2 + 3X3 < 800
4X1 + 3X2 < 480
2X1 + X3 < 320
X3 < 80
X1 , X2 , X3 > 0
b. Excel solution
X1 X2 X3 Total
Decision 45 100 80
Profit $20 $6 $8 $2,140
Resources
X1 X2 X3 Used Capacity
Milling 8 2 3 800 <= 800
Lathes 4 3 480 <= 480
Grinders 2 1 170 <= 320
Sales 1 80 <= 80
c. Solution is X1 = 45 S1 = 0 Z = $2140
X2 = 100 S2 = 0
X3 = 80 S3 = 150
S4 = 0
d. S1 = 0 implies milling machines at capacity
S2 = 0 implies lathes at capacity
S3 = 150 implies grinders not at capacity, with 150 hours available
S4 = 0 implies that X3 is at maximum sales capacity
e. The shadow price for the milling machine department is $2.25 per hour. Since it only cost
$1.50 per hour to work overtime in this department, it is worthwhile to do so. The
allowable increase in overtime is 400; however, only 200 hours are available. Therefore, it
is recommended that 200 hours of overtime in the milling machine department be used.
A-3
© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
APPENDIX A
LINEAR PROGRAMMING USING THE EXCEL SOLVER
1. Excel Solution
X Y Total
Decision 6 0
Profit $3 $1 $18
Resources
X Y Used Capacity
A 12 14 72 <= 85
B 3 2 18 <= 18
C 1 0 <= 4
Graphical solution--the problem requested the Excel solution, but the following graphical
solution is provided for classroom use if desired.
A-1
© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
,Appendix A - Linear Programming Using the Excel Solver
2.
A B Total
Decision 15 10
Cost $2 $4 $70
Resources
A B Used Capacity
A 4 6 120 >= 120
B 2 6 90 >= 72
C 1 10 >= 10
Graphical solution--the problem requested the Excel solution, but the following graphical
solution is provided for classroom use if desired.
A-2
© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
, Appendix A - Linear Programming Using the Excel Solver
3. a. Maximize Z = 20X1 + 6X2 + 8X3
s.t. 8X1 + 2X2 + 3X3 < 800
4X1 + 3X2 < 480
2X1 + X3 < 320
X3 < 80
X1 , X2 , X3 > 0
b. Excel solution
X1 X2 X3 Total
Decision 45 100 80
Profit $20 $6 $8 $2,140
Resources
X1 X2 X3 Used Capacity
Milling 8 2 3 800 <= 800
Lathes 4 3 480 <= 480
Grinders 2 1 170 <= 320
Sales 1 80 <= 80
c. Solution is X1 = 45 S1 = 0 Z = $2140
X2 = 100 S2 = 0
X3 = 80 S3 = 150
S4 = 0
d. S1 = 0 implies milling machines at capacity
S2 = 0 implies lathes at capacity
S3 = 150 implies grinders not at capacity, with 150 hours available
S4 = 0 implies that X3 is at maximum sales capacity
e. The shadow price for the milling machine department is $2.25 per hour. Since it only cost
$1.50 per hour to work overtime in this department, it is worthwhile to do so. The
allowable increase in overtime is 400; however, only 200 hours are available. Therefore, it
is recommended that 200 hours of overtime in the milling machine department be used.
A-3
© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
