Page 184 -

164 CHAPTER 4 LINEAR PROGRAMMING APPLICATIONS

Table 4.12 Advertising Media Alternatives for LDC
Maximum Times Exposure
Number of Potential Cost (£)per Available per Quality
Advertising Media Customers Reached Advertisement Month * Units
1. Daytime TV (1 min) 1 000 1 500 15 65
2. Evening TV (30 sec) 2 000 3 000 10 90
3. Daily newspaper (full 1 500 400 25 40
page)
4. Sunday newspaper 2 500 1 000 4 60
magazine (½ page
colour)
5. Radio, 8:00 A.M.or 300 100 30 20
5:00 P.M. news
(30 sec)
* The maximum number of times the medium is available is either the maximum number of times the advertising medium
occurs (e.g., four Sundays per month or the maximum number of times BP&J recommends that the medium be used).

The data on quality of exposure in Table 4.12 show that each daytime TV (DTV)
advertisement is rated at 65 exposure quality units. Thus, an advertising plan
with DTV advertisements will provide a total of 65DTV exposure quality units.
Continuing with the data in Table 4.12, we find evening TV (ETV) rated at 90
exposure quality units, daily newspaper (DN) rated at 40 exposure quality units,
Sunday newspaper (SN) rated at 60 exposure quality units and radio (R) rated at
20 exposure quality units. With the objective of maximizing the total exposure
quality units for the overall media selection plan, the objective function becomes:

Max 65DTV þ 90ETV þ 40DN þ 60SN þ 20R Exposure quality

We now formulate the constraints for the model from the information given:
9
DTV 15 >
>
>
>
>
ETV 10 >
=
DN 25 Availability of media
>
>
SN 4 >
>
>
>
R 30 ;
1500DTV þ 3000ETV þ 400DN þ 1000SN þ 100R 30 000 Budget

DTV þ ETV 10
Television restrictions
1500DTV þ 3000ETV 18 000
Care must be taken to
ensure the linear 1000DTV þ 2000ETV þ 1500DN þ 2500SN þ 300R 50 000 Customers reached
programming model DTV; ETV; DN; SN; R 0
accurately reflects the
real problem. Always
review your formulation The optimal solution to this five-variable, nine-constraint linear programming model
thoroughly before is shown in Figure 4.6; a summary is presented in Table 4.13.
attempting to solve the
model. The optimal solution calls for advertisements to be distributed among daytime
TV, daily newspaper, Sunday newspaper and radio. The maximum number of
Problem 1 provides exposure quality units is 2370, and the total number of customers reached is
practise at formulating a
similar media selection 61 500. The Reduced Costs column in Figure 4.1 indicates that the number of
model. exposure quality units for evening TV would have to increase by at least 65
Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has
deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.