Question

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:

Time Slot	Cost of advertisement $/min	Estimated number of viewers
Morning	120000	1000000
Afternoon	200000	1300000
Prime Time	400000	3200000
Late Evening	150000	800000

(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?

Answer 1

Solution:

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