decision variable, objective function, constraints

Question

An advertising campaign for a new product will be conducted in Baltimore area and can use TV, radio, magazines, and internet advertisements. Information about each medium is shown below.

Medium                  Cost per Ad                 Number of Customers Reached
TV                          $8000                                        45000
Radio                      $2500                                        13500
Magazines               $3200                                         15200
Internet                  $1000                                         4000

The number of TV advertisements and the number of radio advertisements cannot be more than 10. The number of internet advertisements should be at least as many as the number of advertisements in magazines. There must be at least a total of 20 advertisements in all four media. The advertising budget is $100,000.The objective is to maximize the total number of customers reached.

(a) Define the decision variables.
(b) Determine the objective function. What does it represent?
(c) Determine all the constraints. Briefly describe what each constraint represents.

Note: Do NOT solve the problem after formulating

Answer 1

Manual,

 

You seems to get a lot of these. Are you taking a class that keeps you drilling at it? I think I did this one myself.

 

The decision variables are the amount of money spent on ads in tv, radio, magazines and Internet.

The objective function is the number of customers Reached throughmagazines, ads, tv and radio.

45000t+13500r+15200m+4000i

The constraints are as follows:

 

Total budget 3200m+2500r+8000t+1000I<=100000

At least twenty ads total: m+r+t+I>=20

At least as many Internet ads as thereare magazine ads: I>=m

At most when tv or radio ads: t<=10, r<=10

 

Hope that helps,

Deanna