Management Science Methods

One application of linear programming in marketing is media selection. LP can be used to help marketing

managers allocate a fixed budget to various advertising media. The objective is to maximize reach,

frequency, and quality of exposure. Restrictions on the allowable allocation usually arise during

consideration of company policy, contract requirements, and media availability.

Example:

SMM Company recently developed a new instant salad machine, has $282,000 to spend on advertising.

The product is to be initially test marketed in the Dallas area. The money is to be spent on a TV advertising

blitz during one weekend (Friday, Saturday, and Sunday) in November.

The three options available are: daytime advertising, evening news advertising, and Sunday game-time

advertising. A mixture of one-minute TV spots is desired.

Here is the information regarding the estimated audience reached and cost per ad type:

Ad Type Estimated Audience Reached

with each Ad

Cost per Ad

Daytime 3,000 $5,000

Evening News 4,000 $7,000

Sunday Game 75,000 $100,000

SMM wants to take out at least one ad of each type (daytime, evening-news, and game-time). Further, there

are only two game-time ad spots available. There are ten daytime spots and six evening news spots available

daily. SMM wants to have at least 5 ads per day, but spend no more than $50,000 on Friday and no more

than $75,000 on Saturday.

Considering the above limitations, write a linear programming formulation to help SMM determine the

number for each ad type on the weekend so as to maximize the total audience reached.

Hint 1: You need to define 7 decision variables for daytime and evening news ad on Friday, Saturday and

Sunday as well as a decision variable for Sunday game ad.

Hint 2: Maximize the total audience reached: Max (audience reached per ad of each type) x (number of ads

used of each type)

Hint 3: You need to define A SET of constraints for each of the followings:

– Take out at least one ad of each type

– Ten daytime spots available daily

– Six evening news spots available daily

– At least 5 ads per day

Hint 4: Finally, you need to define a constraint for each of the followings:

– Only two Sunday game-time ad spots available

– Spend no more than $50,000 on Friday

– Spend no more than $75,000 on Saturday

– Spend no more than $282,000 in total

Hint 5: Can you make negative number of ads?

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