the company sells a brand of lowfat shakes that appeal to pe

the company sells a brand of low-fat shakes that appeal to people of all age groups and both genders. The company advertises this shake in a variety of 30-second television ads, and these ads can be placed in a variety of television shows. The ads in different shows vary by cost – some 30-second slots are much more expensive than others – and by the types of viewers they are likely to reach.

The company has segmented the potential viewers into six mutually exclusive categories: males age 18 to 35, males age 36 to 55, males over 55, females age 18 to 35, females age 36 to 55, and females over 55. A rating service can supply data on the numbers of viewers in each of these categories who will watch a 30-second ad on any particular television show. Each such viewer is called an exposure. The company has determined the required number of exposures it wants to obtain for each group. It wants to know how many ads to place on each of several television shows to obtain these required exposures at minimum cost.

The data on costs per ad, numbers of exposures per ad, and minimal required exposures are listed below, where numbers of exposures are expressed in millions, and costs are in thousands of dollars.

What should the company do?

TV Shows

Viewer Group

Game of Thrones

Walking Dead

Homeland

Westworld

Lifetime Evening Movie

The Voice

ESPN

CNN

Minimal Required Exposure

Young Men

3.0

5.0

6.0

5.0

0.1

0.7

0.5

0.1

60

Mid-age Men

5.0

3.0

5.0

2.0

0.1

0.2

0.5

0.2

60

Senior Men

4.0

1.0

3.0

0.0

0.0

0.0

0.3

0.3

28

Young Women

3.0

6.0

1.0

4.0

0.6

0.9

0.1

0.1

60

Mid-age Women

5.0

4.0

1.0

2.0

1.3

0.1

0.1

0.2

60

Senior Women

4.0

2.0

1.0

0.0

0.4

0.0

0.0

0.3

28

Cost per Ad

150.0

140.0

100.0

80.0

15.0

13.0

9.0

8.0

How would you address the fact that multiple ads per show do not translate to multiple exposures for the show?

	TV Shows
Viewer Group	Game of Thrones	Walking Dead	Homeland	Westworld	Lifetime Evening Movie	The Voice	ESPN	CNN	Minimal Required Exposure
Young Men	3.0	5.0	6.0	5.0	0.1	0.7	0.5	0.1	60
Mid-age Men	5.0	3.0	5.0	2.0	0.1	0.2	0.5	0.2	60
Senior Men	4.0	1.0	3.0	0.0	0.0	0.0	0.3	0.3	28
Young Women	3.0	6.0	1.0	4.0	0.6	0.9	0.1	0.1	60
Mid-age Women	5.0	4.0	1.0	2.0	1.3	0.1	0.1	0.2	60
Senior Women	4.0	2.0	1.0	0.0	0.4	0.0	0.0	0.3	28
Cost per Ad	150.0	140.0	100.0	80.0	15.0	13.0	9.0	8.0

Solution

Here, first let us undertand the question.

Lets take example of game of thrones.

Cost per ad of game of thrones is $ 150,000. It serves 24 million exposures in all age groups.

So, cost per exposure is = 0.00625 (150000/24000000). So, cost of one ad for young men group is 0.00625*3000000 = $ 18750

Same way cost per exposure for other ads are:-

2400

Now, for young men for 1 ad the cost is $ 127,205.35

For 1 ad on each show, young men will get 20.4 millions exposure. The minimum required is 60 million.

So, number of ads required for young men to get minimum exposure:-

=60/20.4

=2.94 ads.

Just like that for other age group it is:-

Young men = 2.94

Mid age men = 3.75 (60/16)

Senior men = 3.26 (28/8.6)

Young women = 3.82 (60/15.7)

Mid age women = 4.38 (60/13.7)

Senior women = 3.64 (28/7.7)

So, total ads required = 21.79 ads = 22 ads

Viewer group	game of thrones	walking dead	homeland	westworld	lifetime evening movie	the voice	espn	cnn
young men	18750	33333.33	35294.12	30769.23	600	4792	3000	666.67
mid age men	31250	20000	29400	12308	600	1368	3000	1333.33
senior men	25000	6666.66	17640	0	0	0	1800	2000
young women	18750	40000	5880	24616	3600	6156	600	666.67
mid age women	31250	26666.64	5880	12308	7800	684	600	1333.33
senior women	25000	13333.33	5880	0	2400	0	0	2000
cost per ad	150000	140000	100000	80000	15000	13000	9000	8000