Advertising Budget Decision Making: How to Allocate $100,000 Effectively

What is the appropriate representation of the company's TV advertising budget?

Which set below correctly represents the company's TV advertising budget?

a. { ( x 1 , x 2 , x 3 ) : 100 x 1 + 150 x 2 + 200 x 3 ≥ 100 , 000 }

b. { ( x 1 , x 2 , x 3 ) : 100 x 1 + 150 x 2 , + 200 x 3 = 100 , 000 }

c. { ( x 1 , x 2 , x 3 ) : 100 x 1 + 150 x 2 + 200 x 3 ≤ 100 , 000 }

d. { ( x 1 , x 2 , x 3 ) : 100 x 1 + 150 x 2 + 200 x 3 < 100 , 000 }

Answer:

The appropriate representation of the company's TV advertising budget is { (x1, x2, x3) : 100x1 + 150x2 + 200x3 = 100000 }. This equation states that the total money spent on the ads at each station will exactly equal the company's budget of $100,000.

This equation reflects the fact that the company intends to spend exactly $100,000, distributing this amount among the three TV stations based on their respective advertising rates. Each term (100x1, 150x2, 200x3) represents the cost of advertising on each TV station, multiplied by the number of ads run on that station. The total cost is then equated to the total budget.

The "= 100000" part ensures that the entire budget is utilized, whereas options with inequality signs "<" or "≤" would imply that some of the budget might not be spent, which contradicts the assumption that the company spends the entire $100,000.

By using this equation, the company can make informed decisions on how to allocate its advertising budget effectively, maximizing its reach and impact on the audience.