XYZ Company is planning an advertising campaign for its new product. The media considered are television and radio. Rated exposures per thousand dollars of advertising expenditure are 10,000 for TV and 7,500 for radio. Management has agreed that the campaign cannot be judged successful if total exposures are under 750,000. The campaign would be viewed as superbly successful if 1 million exposures occurred. In addition, the company has realized that the two most important audiences for its product are persons 18 to 21 years of age and persons 25 to 30 years of age. The following table estimates the number of individuals in the two age groups expected to be exposed to advertisements per $ 1,000 of expenditures:

Exposures per $1000

Age Television Radio

1821 2,500 3,000

2530 3,000 1,500

Management has rank ordered five goals it wishes to achieve, arranged from highest to lowest priorities.

Achieve total exposures of at least 750,000 persons.

Avoid expenditures of more than $100,000.

Avoid expenditures of more than $70,000 for television advertisements.

Achieve at least 1 million total exposures.

Reach at least 250,000 persons in each of the two age groups, 1821 and 2530 years. In addition, management realizes and wishes to account for the fact that the purchasing power of the 2530 age group is twice that of the 1821 age group.

Formulate the above decision problem as a single linear goal program. Clearly identify your achievement vector (i.e., hierarchy of priority levels for the goals). Do not solve.