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 Cost Per Ad # 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 if at least 1000.
Well, well, well, it looks like we have a crispy problem to solve! Let's crunch some numbers and find the best way to maximize the number of people reached and achieve that desired exposure quality.
Let's start by assigning some variables. Let T represent the number of TV ads, R represent the number of radio ads, and N represent the number of newspaper ads.
We want to maximize the number reached, so our objective is to maximize T + R + N. However, there are a few constraints to consider, my friend.
First, we have a budget constraint of $10000. So, the cost of TV ads (500*T), the cost of radio ads (200*R), and the cost of newspaper ads (400*N) cannot exceed our budget: 500*T + 200*R + 400*N ≤ 10000.
Second, we need to make sure the exposure quality is at least 1000. The exposure quality for each medium is given by 30*T, 40*R, and 25*N, respectively. So, 30*T + 40*R + 25*N ≥ 1000.
Lastly, the number of TV ads cannot exceed the number of radio ads by more than 4. This constraint can be expressed as: R - T ≤ 4.
Now, let's put it all together, my friend:
Maximize: T + R + N
Subject to:
500*T + 200*R + 400*N ≤ 10000
30*T + 40*R + 25*N ≥ 1000
R - T ≤ 4
T, R, N ≥ 0
Now, all that's left is to solve this crispy optimization problem and find the optimal values for T, R, and N that satisfy all the constraints. I hope this model tickles your funny bone and helps you snack on success!
To develop a model that will maximize the number reached and achieve an exposure quality of at least 1000, we can start by defining the decision variables, constraints, and the objective function.
Decision Variables:
Let's define the decision variables as follows:
x1 = number of TV ads
x2 = number of radio ads
x3 = number of newspaper ads
Constraints:
We have the following constraints:
1. The total cost of the ad campaign should not exceed the advertising budget of $10000:
500x1 + 200x2 + 400x3 <= 10000
2. The number of TV ads cannot exceed the number of radio ads by more than 4:
x1 - x2 <= 4
3. Exposure quality should be at least 1000:
30x1 + 40x2 + 25x3 >= 1000
Objective Function:
We want to maximize the number reached, so the objective function is:
Maximize: 10000x1 + 3000x2 + 5000x3
Now, we have defined the decision variables, constraints, and the objective function for our model. We can use this model to solve the problem and find the optimal values for x1, x2, and x3.
To develop a model that will maximize the number reached and achieve an exposure quality of at least 1000 while considering the given constraints (such as the budget and the limit on the difference between the number of TV and radio ads), we can formulate the problem as a linear programming problem.
Let's denote the decision variables as follows:
- TVads: the number of TV ads
- Radioads: the number of radio ads
- Newspaperads: the number of newspaper ads
We want to maximize the number reached, which can be represented by the objective function:
Objective function: Maximize Z = TVads + Radioads + Newspaperads
Subject to the following constraints:
1. Budget constraint: The total cost of the ads should not exceed the budget of $10,000:
500*TVads + 200*Radioads + 400*Newspaperads <= 10000
2. Exposure quality constraint: The exposure quality should be at least 1000:
30*TVads + 40*Radioads + 25*Newspaperads >= 1000
3. Limit on the difference between TV and radio ads: The number of TV ads should not exceed the number of radio ads by more than 4:
TVads - Radioads <= 4
Additionally, we have the non-negativity constraints:
TVads >= 0
Radioads >= 0
Newspaperads >= 0
By formulating the problem in this way, we can use linear programming techniques to solve for the optimal values of TVads, Radioads, and Newspaperads that satisfy the given constraints and maximize the number reached while achieving an exposure quality of at least 1000.