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 CostPerAd # 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 of at least 1000.
a. set up the problem (provide the objective function and set of constraints)
b. find the optimal solution
c. list the values of the objective function and the decision variables in the optimal solution you’ve found.
Incomplete.
dkfkh
adkklqjd
a. Objective function:
The objective is to maximize the number of people reached while achieving an exposure quality of at least 1000.
Set of constraints:
1. The advertising budget is $10,000.
2. The number of TV ads cannot exceed the number of radio ads by more than 4.
3. The exposure quality should be at least 1000.
Decision Variables:
Let's denote the number of TV ads as "x", the number of radio ads as "y", and the number of newspaper ads as "z".
b. To find the optimal solution, we need to write the objective function and the set of constraints mathematically.
Maximize: 10000x + 3000y + 5000z (number of people reached)
Subject to:
1. 500x ≤ 10000 (cost constraint for TV ads)
2. 200y ≤ 10000 (cost constraint for radio ads)
3. 400z ≤ 10000 (cost constraint for newspaper ads)
4. x - y ≤ 4 (constraint on the difference between TV ads and radio ads)
5. 30x + 40y + 25z ≥ 1000 (exposure quality constraint)
c. To find the optimal solution, this mathematical model should be solved using an optimization method or software. The values of the decision variables and the objective function in the optimal solution can be obtained from the solution to the mathematical model.