Question

Question 4 options:

The Rapid City Chamber of Commerce periodically sponsors public service seminars and programs which are open to the public. Currently, promotional plans are under way for this year’s program. Advertising alternatives include television, radio, and newspaper. Audience estimates, costs, and maximum media usage limitations are shown below:

	Television	Radio	Newspaper
Audience per advertisement	80,000	15,000	30,000
Cost per advertisement	$1,900	$290	$510
Maximum media usage limitation	15	25	10

Suppose that the production budget is limited to $39,000. We are limited to run at most 41 Ads in all three mediums combined. We need to determine how many commercial messages should be run on each medium so as to reach as many people in Rapid City as possible.

Optimal Solution:
Number of TV Ads =

Number of Radio Ads =

Number of Newspaper Ads =

Total Audience Reached =

Hint: Value should be between 1735300 and 1741200
The Total Cost to buy all of these Ads will be $

Answer 1

Let the number of TV ads be x, Radio ads be y and Newspaper ads be z

Total Audience reached = 80,000x + 15000y + 30000z

We have to maximize this number

Total Budget = $39000

Total cost = 1900x + 290y + 510z

Hence, we get constraint as:

1900x + 290y + 510z <= 39000

Further, we get constraints based on no. of ads allowed:

x + y + z <= 41

x <= 15

y <= 25

z <= 10

x, y, z >= 0 as no. of ads cannot be negative

We solve the above in Excel using Excel Solver as shown below:

The above solution in the form of formulas along with Excel Solver extract is shown below for better understanding and reference:

As seen from above,

Optimal Solution:

Number of TV Ads = 15 nos.
Number of Radio Ads = 16 nos.
Number of Newspaper Ads = 10 nos.
Total Audience Reached = 1740000
The Total Cost to buy all of these Ads will be $38,240 as seen from LHS for Constraint 1 for Budget

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