Question

An ad campaign for a new snack chip will be conducted in a limited geographical area and can use TV
time, radio time and newspaper ads. Information about each medium is shown below.

Medium Cost Per Ad # Reached Exposure Quality
TV 500 10000 30
Radio 200 3000 40
Newspaper 400 5000 25

If the number of TV ads cannot exceed the number of radio ads by more than 4, and if the advertising budget is $10000, develop the model that will maximize the number reached and achieve an exposure quality if at least 1000.

Answer 1

Let x number of TV ads. Let y number of radio ads Let znumber of newspaper ads Then the chart looks like this: Medium TV (x) Radio (y) News (z) Total Cost Per Ad No. reached Exp. Quality 10,000r 3. 000у 5,000z 500x 200y 400z 10, 000 30T 40y 25z 1,000 And we have these inequalities 冫>0 500x +200y + 400z 10, 000 30 40y 50z 1,000 Objective function: N10,000r + 3,000y 5,000z

The solver gives the following output for the optimization -

x	y	z
14.28571	14.28571	0	185714.3
7142.857	2857.143	0	10000	<=	10000
428.5714	571.4286	0	1000	>=	1000
14.28571	14.28571		-4	<=	0

So, the maximum value is = 185714.3.