A local business plans on advertising their new product by p

A local business plans on advertising their new product by purchasing advertisements on theradio and on TV. The business plans to purchase at least 60 total ads and they want to have atleast twice as many TV ads as radio ads. Radio ads cost $20 each and TV ads cost $80 each.The advertising budget is $4320. It is estimated that each radio ad will be heard by 2000listeners and each TV ad will be seen by 1500 people. How many of each type of ad should bepurchased to maximize the number of people who will be reached by the advertisements?

Modeling the Problem:

1. Let X be the number of radio ads that are purchased and Y be the number of TV ads.1.  Write down a linear inequality for the total number of desired ads.

2. Write down a linear inequality for the cost of the ads.

3. Recall that the business wants at least twice as many TV ads as radio ads. Write down alinear inequality that expresses this fact.

Solution

1)

Let X be the number of radio ads that are purchased and Y be the number of TV

x+y >=60

2)  

20x+80y <= 4320

3. ) the business wants at least twice as many TV ads as radio ads.

y > = 2x

Further x>=0 and y>=0

The function for the number of people that will be exposed to the advertisements:

P = 2000x +1500y