As part of a campaign to promote its annual clearance sale, a company decided to buy television-advertising time on a TV station. Company's television-advertising budget is $102,000. Morning time costs $3,000/minute, afternoon time costs $1,000/minute, and evening (prime) time costs $12,000/minute. Because of previous commitments, the station cannot offer the company more than 7 min of prime time or more than a total of 25 min of advertising time over the 4 wk in which the commercials are to be run. The station estimates that morning commercials are seen by 210,000 people, afternoon commercials are seen by 105,000 people, and evening commercials are seen by 630,000 people. How much morning, afternoon, and evening advertising time should the company buy to maximize exposure of its commercials? What is the maximum number of viewers?
A) 22 min of morning advertising time, 0 min of afternoon advertising time, 3 min of evening advertising time; 6.51 million viewers
B) 10 min of morning advertising time, 15 min of afternoon advertising time, 0 min of evening advertising time; 4.4 million viewers
C) 16 min of morning advertising time, 7 min of afternoon advertising time, 2 min of evening advertising time; 5 million viewers
D) 15 min of morning advertising time, 3 min of afternoon advertising time, 7 min of evening advertising time; 5.67 million viewers

Question

Quizplus · Accepted Answer

To maximize exposure, the company should allocate its budget to achieve the highest total viewership within the given constraints. By purchasing 22 minutes of morning time ($66,000), 0 minutes of afternoon time ($0), and 3 minutes of evening time ($36,000), the company utilizes its entire budget of $102,000 and adheres to the time constraints. This strategy results in 6.51 million viewers, calculated as (22 min * 210,000 viewers) + (0 min * 105,000 viewers) + (3 min * 630,000 viewers).

As Part of a Campaign to Promote Its Annual Clearance