McDonald and Thomas Advertising Agency has been hired to put together an adverti
ID: 3045939 • Letter: M
Question
McDonald and Thomas Advertising Agency has been hired to put together an advertising plan for the Healthy Heart Charity Banquet. The advertising media under consideration are listed in the table below:
Medium
Cost Per Use
Effective Audience Reached
Maximum Number of times Available
Outdoor
$500
2000
3
Radio
$100
800
10
Newspaper
$200
1500
2
TV Commercial
$1000
3000
4
PSA
0
500
*
* The TV station will award up to three public service announcements (PSA) for each commercial purchased.
The budget for the campaign is $6000. Every medium must be used at least once. The total number of appearances on TV (including PSA) should be no more than twice the number of all the other advertisements. Develop a linear programming model that list objective function and constraints to maximize the effective audience reached. Use integer programming to make the variables in whole numbers. Use Lindo to solve all problems.
Please do not show solution to problem in Excel Solver. Please simply show how to derive the objective function and constraint functions.
Medium
Cost Per Use
Effective Audience Reached
Maximum Number of times Available
Outdoor
$500
2000
3
Radio
$100
800
10
Newspaper
$200
1500
2
TV Commercial
$1000
3000
4
PSA
0
500
*
Explanation / Answer
outdoor - x1
radio - x2
newspaper - x3
TV commercial - x4
PSA - x5
Z = 2000*x1 + 800*x2 +1500 *x3 + 3000* x4 + 500*x5
x1 >= 1
x2 >= 1
x3 >= 1
x4 >= 1
x5 >= 1
x1 <= 3
x2 <= 10
x3 <= 2
x4 <= 4
cost = 500*x1 + 100*x2 + 200*x3 + 1000x4 <= 6000
x4 <= 2*(x1+x2+x3+x5)