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MARKETING AND MEDIA APPLICATIONS 165

before this media alternative could appear in the optimal solution. Note that the
budget constraint (constraint 6) has a dual price of 0.060. Therefore, a £1.00
increase in the advertising budget will lead to an increase of 0.06 exposure
quality units. The dual price of 25.000 for constraint 7 indicates that reducing
the number of television commercials by one will increase the exposure quality
of the advertising plan by 25 units. Thus, LDC should consider reducing the
More complex media requirement of having at least ten television commercials.
selection models may A possible shortcoming of this model is that, even if the exposure quality measure
include considerations were not subject to error, it offers no guarantee that maximization of total exposure
such as the reduced
exposure quality value for quality will lead to a maximization of profit or of sales (a common surrogate for
repeat media usage, cost profit). However, this issue is not a shortcoming of linear programming; rather, it is
discounts for repeat a shortcoming of the use of exposure quality as a criterion. If we could directly
media usage, audience
overlap by different measure the effect of an advertisement on profit, we could use total profit as the
media and/or timing objective to be maximized.
recommendations for the
advertisements.
Figure 4.6 The Management Scientist Solution for the LDC Problem
Objective Function Value = 2370.000
Variable Value Reduced Costs
-------------- --------------- -----------------
DTV 10.000 0.000
ETV 0.000 65.000
DN 25.000 0.000
SN 2.000 0.000
R 30.000 0.000

EXCEL file Constraint Slack/Surplus Dual Prices
LOCHSIDE -------------- --------------- ----------------
Media
1 5.000 0.000 Availability
2 10.000 0.000
3 0.000 16.000 Budget
4 2.000 0.000
5 0.000 14.000 Television
6 0.000 0.060 Restrictions
7 0.000 –25.000
8 3000.000 0.000 Audience
9 11500.003 0.000 Coverage

Table 4.13 Advertising Plan for LDC

Media Frequency Budget
Daytime TV 10 £15 000
Daily newspaper 25 10 000
Sunday newspaper 2 2 000
Radio 30 3 000
£30 000
Exposure quality units ¼ 2 370
Total customers reached ¼ 61 500

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