Milson Company is planning using advertisement for its produ

Milson Company is planning using advertisement for its product during the coming month. Five media are being considered with a budget of $50,000. Some of the restrictions are: at least 15 television commercials must be used, at least $60,000 potential customers must reached, and no more than $20,000 may be spent on television advertisements. Below is the summary of related information.

The company would like to get a reasonable advertising media selection plan with the objective of maximizing the total exposure quality units for the selection. Your job is to set up a linear programming model for the problem. (Define your decision variables first).

Advertising Media Numberof Potential Customers Researched Cost per Advertisment Max Times Available Exposure Quality Units DaytimeTv Evening TV Daily Newspaper Sunday Newspape Radio 1500 $ 2500$ 2000 $ 3000 $ 500 $ 1,800.CO 4,0C0CO 8CALCO 1,5tl.CO COLCO 20 18 30 6 40 80 100 50 80 30

Solution

the decision variables are as follows:

for the TV

let the number of daytime ads be = x

and the number of evening adds by = y

for the newsaper

the number of daily newspaper adds be = z

and the number of sunday newsparer ads by = w

for the radio

ads for the radio be = u

=> the constraints are:

the budget is of $ 50000 for the advertizments is:

1800 x + 4000y + 800z + 1500w + 200u <= 50000

there need to atleast 15 TV ads:

x + y >= 15

no more that $ 20000 are to spend on TV ads:

1800x + 4000y <= 20000

atleast 60000 customers need to be reached:

1500x + 2500y + 2000z + 3000w + 500u >= 60000

the objective function is given by:

Z = 80x + 100y + 50z + 80w + 30u