Chapter 8
Linear Programming
Applications
Focus of This Chapter
• Formulating a practical problem into a
linear program.
• Recall that “formulating” is to re-describe
the problem in terms of linear program.
• Formulating is “translating”, not “solving”!
• Computer will do the “solving” part.
Media Selection
Medium
TV
Newspaper
Radio (prime
time)
Radio (afternoon)
Audience
reached / ad
5,000
8,500
Cost /
ad ($)
800
925
Max ads
per week
12
5
2,400
290
25
2,800
380
20
• Budget up to $8,000
• At least 5 radio spots
• Cost of radio ads is no more than $1,800 per week
How many ads of each type should be used to max
audience reached?
Media Selection with reorganized data
Medium
TV
Newspa
per
Radio
(prime
time)
Radio
(afternoon)
Audience
reached / ad
5,000
8,500
2,400
2,800
Cost / ad ($)
$800
$925
$290
$380
Max ads per
week
12
5
25
20
Others
•At least 5 radio ads
•Radio cost no more
than 1,800
Budget
per
week
$8,000
Marketing Research
• How many peoples grouped in ‘age’ and ‘region’ should
be surveyed to minimize total cost?
• Requirements of survey:
–
–
–
–
–
At least 2,300 households in total
At least 1,000 w/ ’30 or younger’
At least 600 w/ ’31-50’
At least 15% in ‘bordering states’
No more than 20% in ‘bordering states’ and ’51 or older’
• Cost per person surveyed:
30 or younger
31-50
50 or older
Bordering Mexico
$7.50
$6.80
$5.50
Not bordering Mexico
$6.90
$7.25
$6.10
Region