Numbers English Contest #16

A car manufacturer is testing out an advertising campaign by using a local TV station. It has identified a particular evening TV show it feels will reach its target audience. The car manufacturer wants to run a half million impressions in the next month to see how this campaign affects sales in this area. If the campaign is successful, it will expand this campaign nationally.

The area serves 240,000 people. The ratings for this TV show are 2.41% of the total population. TV commercials for that show run for $315 for a 30-second spot. How much will it cost to run this test advertising campaign? If the manufacturer's profit is $825 per car sold, how many cars must be sold just to pay for this advertising campaign?   

Solution to Contest #15

First, we take a look at what the questions is asking for.

Which campaign is most effective for Dave, based on a cost per 1000 impressions?

Note that the question did not ask for cost per click.

Next we calculate the cost per 1000 impressions for Campaign #1.

$31.00 / 40,134 x 1000 = $0.772 per thousand impressions.

Next, we do some calculations for Campaign #2. We must think a little to use the information relating to "clicks" appropriately.

Cost = $31.00 x 2.1 = $63.00

Clicks = 158

Click Through Rate = 0.92% = 0.0092

Impressions = 158/0.0092=17,174

Cost per 1000 impressions = $63.00 / 17,174 x 1000 = $3.67 per thousand impressions.

Next, we do some calculations for Campaign #3. 

Cost = $31.00 - $12.25 = $18.75

Clicks = 158 * (1-0.115) = 140

Click Through Rate = 0.92% + 0.54% = 1.46% = 0.0146

Impressions = 140/0.0146 = 9,589

Cost per 1000 impressions = $18.75 / 9,589 x 1000 = $1.96 per thousand impressions. 

Campaign #1 is the most effective campaign, based on cost per thousand impressions.