In: Math
An athletic footwear company is attempting to estimate the sales
that will result from a television advertisement campaign of its
new athletic shoe. The contribution to earnings from each pair of
shoes sold is $40. Suppose that the probability that a television
viewer will watch the advertisement (as opposed to turn his/her
attention elsewhere) is 0.40. Furthermore, suppose that 1% of
viewers who watch the advertisement on a local television channel
will buy a pair of shoes. The company can buy television
advertising time in one of the time slots according to Table
below:
Television advertising costs and viewers
Time Slot | Cost of Advertisement ($/minute) | Estimated number of viewers |
Morning | 120,000 | 1,000,000 |
Afternoon | 200,000 | 1,300,000 |
Prime Time | 400,000 | 3,200,000 |
Late evening | 150,000 | 800,000 |
(a) Suppose that the company decides to buy one minute of
advertising time. Which time slot would yield the highest expected
contribution to earnings net of costs? What is the total expected
contribution to earnings resulting from the advertisement?
(b) Suppose the company decides to buy two one-minute
advertisements in different time slots. Which two different time
slots should the company purchase to maximize the expected
contribution to earnings? What is the total expected contribution
to earnings resulting from these two advertisements?
For this, we need to do the cost-benefit analysis for all the four slots
For example,
time slot: morning
Estimated number of viewers = 1000000
Number of viewers would watch the advertisement = 0.4*1000000 = 400,000
number of people will buy the shoes = 0.01*400000 = 4000
Therefore, contribution to earnings resulting from advertising in the morning slot = 4000*40 - 120000 = 40000
time slot: Afternoon
Estimated number of viewers = 1300000
Number of viewers would watch the advertisement = 0.4*1300000 = 520,000
number of people will buy the shoes = 0.01*520000 = 5200
Therefore, contribution to earnings resulting from advertising in the morning slot = 5200*40 - 200000 = 8000
time slot: prime time
Estimated number of viewers = 3200000
Number of viewers would watch the advertisement = 0.4*3200000 = 1280,000
number of people will buy the shoes = 0.01*1280000 = 12800
Therefore, contribution to earnings resulting from advertising in the morning slot = 12800*40 - 400000 = 112000
time slot: late evening
Estimated number of viewers = 800000
Number of viewers would watch the advertisement = 0.4*800000 = 320,000
number of people will buy the shoes = 0.01*320000 = 3200
Therefore, contribution to earnings resulting from advertising in the morning slot = 3200*40 - 150000 = -22000
Therefore, the first best time slot is "prime time" with the contribution to earnings = 112000
the next best slot is "morning" with the contribution to earnings = 40000