Question

Amanda has a yearly advertising and promotions budget of $50,000. Her goal is to maximize the reach (the number of customers that see her company’s ads or other marketing efforts). She is considering a mix of placing ads on art websites and in printed art magazines, as well as using targeted social media ad placements and appearances at art tradeshows. She wants to make sure that the company has an online presence, so would like to see at least 100 ads placed in any combination of websites and social media per year. However, she has data that suggests that if she advertises on the websites more than 60 times per year she will be wasting money. There are seven art tradeshows that the company could attend, but Amanda feels it is mandatory to attend at least the two most popular tradeshows. There are three major art magazines, each published monthly, that Amanda would like to advertise in. She could advertise in each of these once per month but would be comfortable reducing the frequency to a minimum of once every three months in each magazine and rotating the placements between the magazines. The reach and cost of each type of ad placement or event is shown below: Art Websites Social Media Art Tradeshows Print Magazine Ads Reach (number of people) 20,000 10,000 5,000 15,000 Cost (dollars) 200 250 1,000 400 Recommend the appropriate mix of advertising and promotions for the company. Also comment on what would change if Amanda doubled her advertising and promotions budget. Estimate the increased reach.

Answer 1

Solution:

Let us assume that number of advertisements or events on each of the four channels are as follows:

1. Art Websites = a
2. Social Media = b
3. Art Tradeshows = c
4. Print Magazines = d

Now it is given that reach and cost of each channel is as follows:

Advertising Channel	Ads Reach (Number of People)	Cost (Dollars)
Art Websites	20,000	200
Social Media	10,000	250
Art Tradeshows	5,000	1,000
Print Magazines	15,000	400

Amanda’s objective is to maximize the reach. So, we can say that the goal is to –

Maximize           z             =            (20,000 . a)        +            (10,000 . b)        +              (5,000 . c)           +            (15,000 . d)

Or we can rewrite it for thousands of people as follows:

Maximize           z             =            20.a + 10.b + 5.c + 15.d

Amanda has a yearly advertising and promotions budget of $50,000. Hence –

200.a + 250.b + 1000.c + 400.d ≤ 50000

»            4.a + 5.b + 20.c + 8.d ≤ 1000

Amanda would like to see at least 100 ads placed in any combination of websites and social media per year. Hence –

a + b ≥ 100

If she advertises on the websites more than 60 times per year she will be wasting money. Hence –

a ≤ 60

There are seven art tradeshows that the company could attend, but Amanda feels it is mandatory to attend at least the two most popular tradeshows. Hence –

c ≤ 7      and

c ≥ 2

There are three major art magazines, each published monthly. Hence –

d ≤ (3*12)

»            d ≤ 36

Now Amanda is comfortable reducing the frequency to a minimum of once every three months in each magazine and rotating the placements between the magazines. Hence –

d ≥ (3*4)

»            d ≥ 12

So, we can solve it using integer programming as follows:

Maximize           z             =            20.a + 10.b + 5.c + 15.d

Subject to

              4.a + 5.b + 20.c + 8.d ≤ 1000

              a + b ≥ 100

              0 ≤ a ≤ 60

              0 ≤ b

              2 ≤ c ≤ 7

              12 ≤ d ≤ 36

Now, solving it using excel solver, we would find following as the optimal mix –

a = 60, b = 124, c = 2, 12               ANSWER

Reach = (20*60) + (10*124) + (2*5) + (15*12)      Thousands

              =            2,630,000           ANSWER

Please observe that

1. We will use maximum possible value of a (Websites), i.e. 60, since it generates maximum reach (20,000) in minimum investment (4,000).
2. We will keep c and d, i.e. Tradeshows and Magazines to a minimum since they generate minimum reach in maximum investment.
3. Rest all the funds will be used to generate reach using Social Media, as there is no restriction on that. Moreover, it is almost the lowest cost option with a bigger reach.

Hence if we double the advertising budget. The optimal mix will be derived by changing following constraint-

              4.a + 5.b + 20.c + 8.d ≤ 2000 (Doubled)

And the optimal mix in double budget would be –

a = 60, b = 324, c = 2, 12 (following the strategy of maximizing social media spend) ANSWER

And the increased Reach = (20*60) + (10*324) + (2*5) + (15*12) Thousands              =            4,630,000           ANSWER