Question

The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown: Constraint Television Radio Online Audience per advertisement 110,000 18,000 30,000 Cost per advertisement $1,500 $250 $500 Maximum media usage 11 21 13 To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized.

(a) If the promotional budget is limited to $23,000, how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter “0”. Advertisement Alternatives No of commercial messages Television Radio Online What is the allocation of the budget among the three media? Advertisement Alternatives Budget ($) Television $ Radio $ Online $ What is the total audience reached?

(b) By how much would audience contact increase if an extra $100 were allocated to the promotional budget? Round your answer to the nearest whole number. Increase in audience coverage of approximately

Answer 1

Given,

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Audience for Television Ad = 110000

Audience for Radio Ad = 18000

Audience for Online Ad = 30000

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Cost for Television Ad = $1500

Cost for Radio Ad = $250

Cost for Online Ad = $500

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Maximum Media Usage Television = 11

Maximum Media Usage Radio = 21

Maximum Media Usage Online = 13

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Let be the Television, Radio and Online Usages.

Then we require that

Now, we also require that, radio advertisements not exceed 50% of total ads. i.e.

or,

Also, we require that televsion should account for atleast 10% of total ads i.e.

or,

The total budget is $23000. Therefore,

or,

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(a) We have to maximize the total audience contact. This problem can be formulated as LP as follows

max.

s.t.

Here is the screenshot of the Excel Sheet used to solve this LP

Here is the solver configuration

Upon Solving we get-

Television Usage	11
Radio Usage	16
Online Usage	5
Total Audience Contact	1648000
Total Cost	$23000

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(b) If an extra $100 were allocated, we simply change the budget constrained to account for this and get the solution

Television Usage	11
Radio Usage	16
Online Usage	5
Total Audience Contact	1648000
Total Cost	$23000

Clearly, $100 is not enough to account for any changes in the allocation and therefore the audience contact is the same.