The Westchester Chamber of Commerce periodically sponsors public service seminar

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 newspaper. Audience estimates, costs, and maximum media usage limitations are as shown:

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.

If the promotional budget is limited to $29,300, how many commercial messages should be run on each medium to maximize total audience contact? What is the allocation of the budget among the three media? If required, round your answers to the nearest dollar.

What is the total audience reached? Round your answer to the nearest whole number.

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.

Constraint Television Radio Newspaper Audience per advertisement 100000 18000 20000 Cost per advertisement $2000 $300 $600 Maximum media usage 10 20 10

Explanation / Answer

SOLVING THE MODEL IN EXCEL SOLVER:

D) sensitivity report:

In sensitivity report, for the budget constraint, Lagrange Multiplier of 42.22 implies, with $1 increase in the budget the audience reached will increase by 42.22.

For $100 increase in budget, audience reached will increase by 42222 (=42.22*100(rounded off))

Hence, the audience reached if budget is increased by $100 = 1488222

Constraint Television Radio Newspaper Audience per advertisement        1,00,000         18,000            20,000 Cost per advertisement ($)              2,000               300                  600 Maximum media usage                    10                 20                    10 NO OF ADS T R N CONSTRAINTS: R < = 0.50* (T+R+N) T > = 0.10*(T+R+N) T<=10 (MAX MEDIA USAGE ) R<=20 N<=10 2000*T+300*R+600*N<=29300 (BUDGET) OBJECTIVE FUNCTION: MAXIMIZE (TOTAL AUDIENCE CONTACT) TOTAL AUDIENCE CONSTACT = 100000T+18000R+20000N

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