Question

A candidate for mayor in a small town has allocated

$40,000 for last-minute advertising in the days pre-

ceding the election. Two types of ads will be used:

radio and television. Each radio ad costs $200 and

reaches an estimated 3,000 people. Each television

ad costs $500 and reaches an estimated 7,000 people.

In planning the advertising campaign, the campaign

manager would like to reach as many people

as possible, but she has stipulated that at least 10 ads

of each type must be used. Also, the number of radio

ads must be at least as great as the number of television

ads. How many ads of each type should be

used? How many people will this reach?

Answer 1

Let the No. of Radio ads be R and no. of TV ads be T

Total Reach = 3000R + 7000T

We have to maximize this total reach

Subject to constraint

200R + 500T <= 40,000.............Constraint for cost per ad and budget allocated

R >= 10.......................................Constraint for minimum no. of radio ads

T >= 10.......................................Constraint for minimum no. of TV ads

R >= T.........................................Constraint that no. of radio ads at least equal to no. of TV ads

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

Each type of ads are:

Radio ads = 175 ads

TV ads = 10 ads

No. of people reached = 595,000 people

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

-----------------------------------------------------------------------------------------------------------------------

In case of any doubt, please ask through the comment section before Upvote/downvote.

If you liked the answer, please give an upvote. This will be quite encouraging for me, thank-you!!!