Question

A marketing manager wishes to allocate his annual advertising budget of $1.5 million in three media: television (TV), radio, and daily newspaper. The unit cost of an advertisement in TV is $10,000, in radio $5,000, and in newspaper $3,000. The company advertises in one TV channel, one radio station, and one newspaper only. The number of advertisements in each media must be at least 20. The expected effective 52 Optimization Modelling: A Practical Approach audience for each advertisement for TV is 30,000, for radio 18,000, and for newspaper 10,000. Develop a mathematical model.

Answer 1

Let 'T', 'R', 'N' be the number of advertisements on TV, Radio, and Newspapers respectively.

Maximize Z = overall effective audience = 30000*T + 18000*R + 10000*N

Subject to,

10000*T + 5000*R + 3000*N <= 1500000 (Budget constraint)

T >= 20 (min T)

R >= 20 (min R)

N >= 20 (min N)

T, R, N >= 0