Chapter 8
LP Modeling
Applications:
With Computer
Analyses in Excel
and QM for
Windows
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
8-1
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Learning Objectives
Students will be able to
• Model a wide variety of medium to
large LP problems.
• Understand major application areas,
including marketing, production, labor
scheduling, fuel blending,
transportation, and finance.
• Gain experience in solving LP problems
with QM for Windows and Excel
Solver software.
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
8-2
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Chapter Outline
8.1 Introduction
8.2 Marketing Applications
8.3 Manufacturing Applications
8.4 Employee Scheduling
Applications
8.5 Financial Applications
8.6 Transportation Applications
8.7 Transshipment Applications
8.8 Ingredient Blending
Applications
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
8-3
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Marketing
Applications
Media Selection:
Win Big Gambling Club
Medium
Audience Cost Maximum
Reached Per Ads Per
Per Ad Ad($) Week
TV spot (1 minute)
5,000
800
12
Daily newspaper
(full page ad)
8,500
925
5
2,400
290
25
2,800
380
20
Radio spot (30
seconds,
prime time)
Radio spot
(1 minute,
afternoon)
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
8-4
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Win Big Gambling
Club
Maximize : 5000 X1 + 8500 X 2
Subject to :
+ 2400 X 3 + 2800 X 4
X 1  12 (max TV spots/week)
X 2  5 ( max newspaper ads/week)
X 3  25 ( max 30 - sec. radio spots/week)
X 4  20 (max 1 - min. radio spots/week)
800 X1 + 925 X 2 + 290 X 3 + 380 X 4  8000
(Weekly ad budget)
X 3 + X 4  5 (min radio spots/week)
290X3 + 380X4  1800(max radio expense)
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
8-5
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Win Big Gambling
Club - QM for
Windows
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
8-6
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Manufacturing
Applications
Production Mix - Fifth Avenue
Variety Selling Monthly Monthly Material Material
of Tie Price per Contract Demand Required RequireTie ($) Minimum
per Tie ments
(Yds)
All silk
6.70
6000
7000
0.125
All
3.55
polyester
Poly4.31
cotton
blend 1
10000
14000
0.08
13000
16000
0.10
6000
8500
0.10
Polycotton blend 2
4.81
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
8-7
100%
silk
100%
polyester
50%
poly/50%
cotton
30%
poly/70%
cotton
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Fifth Avenue
Maximize: 4.08X1 + 3.07X2 + 3.56X3 + 4.00X4
Subject to :
0 .125 X1  800 (yards of silk)
0 .08 X 2 + 0 .05 X 3 + 0 .03 X 4  3000 (yards polyester)
0 .05 X 3 + 0 .07 X 4  1600 (yards cotton)
X1  6000 (contract min, silk)
X1 7000 (contract max, silk)
X 2  1000 (contract min, all polyester)
X 2  14000 (contract max, all polyester)
X 3  13000 (contract min, blend 1)
X3  16000 (contract max, blend 1)
X 4  6000 (contract min, blend 2)
X 4  8500 (contract max, blend 2)
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
8-8
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Fifth Avenue QM for
Windows
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
8-9
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Manufacturing
Applications
Truck Loading - Goodman Shipping
Item
Value
($)
Weight
lbs
1
22,500
7,500
2
24,000
7,500
3
8,000
3,000
4
9,500
3,500
5
11,500
4,000
6
9,750
3,500
3,500
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
8-10
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Goodman Shipping
Maximize load value: 22500X1 +24000 X2 +8000X3
+9500 X +11500 X +9750 X
4
5
6
Subject to:
:
7500 X1 +7500X2 +3000X3 +3500X4 +4000X5
+3500 X 10000 (Capacity)
6
X11
X2 1
X3 1
X4 1
X5 1
X6 1
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
8-11
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Goodman Shipping Excel
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
8-12
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Goodman Shipping Excel
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
8-13
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Manufacturing
Applications
Blending Problem:
- Low Knock Oil Company
Crude
A(%)
B(%)
Oil
Cost/Barrel
($)
Type
X100
35
55
30.00
X220
60
25
34.80
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
8-14
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Low Knock Oil
Company
Minimize 30X1 + 30X2 + 34.80X3 + 34.80X4
Subject to:
X1 + X3  25000
X2 + X4  32000
-0.10 X1 + 0.15X3  0
0.05X2 – 0.25X4  0
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
8-15
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Low Knock Oil
Company QM for
Windows
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
8-16
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458