Answer:
The solution is given as such that ads run on Television, Radio and Online are 10, 4 and 10 respectively for the maximum audience of 1472000 such that the budget allocation is 14000, 1200 and 6000 between Television, Radio and Online respectively.
Explanation:
For the constraint analysis the data is given as below
Constraint Television Radio Online
Audience 100000 18000 40000
Cost $1400 $300 $600
Max Media 10 20 10
Let's suppose
- the number of Television advertisements as T
- the number of Radio advertisements as R
- the number of Online advertisements as O
So the function to maximize is given as
Z=100000T+18000R+40000O
The constraints are
1400T+300R+600O ≤21200
T≤10
R≤20
O≤10
Radio advertisements must not exceed 50% of the total number of advertisements authorized.
R≤0.5(T+R+O)
In addition, television should account for at least 10% of the total number of advertisements authorized.
T≥0.1(T+R+O)
Using the following spreadsheet the solution is obtained using following steps
- Data is entered as given in the attached screenshot.
- Than from the Data tab solver is selected and following values are arranged accordingly as shown in the screen shot. (if the solver option is not visible in the data tab, check whether the addon is available from the file>options>manage add-ons as shown in the screen shot. If the solver option is available, than from the Developer tab enable the option from Excel Add-ons and than you would be able to see the Data Solver tab)
- Input the different values as shown in the attached file
The solution is given as such that
T=10
R=4
O=10
The total maximized audience is 1472000
The budget allocation is 14000, 1200 and 6000 between Television, Radio and Online respectively.
