Management Science Methods

Marketing Application-Media Selection

1. Define the decision variables

DFR = number of daytime ads on Friday

DSA = number of daytime ads on Saturday

DSU = number of daytime ads on Sunday

EFR = number of evening ads on Friday

ESA = number of evening ads on Saturday

ESU = number of evening ads on Sunday

GSU = number of game-time ads on Sunday

2. Define the Objective Function

Maximize the total audience reached: Max (audience reached per ad of each type) x (number of ads

used of each type)

Max 3000DFR +3000DSA +3000DSU +4000EFR+4000ESA +4000ESU +75000GSU

3. Define the Constraints

Take out at least one ad of each type:

(1) DFR + DSA + DSU > 1

(2) EFR + ESA + ESU > 1

(3) GSU > 1

Ten daytime spots available:

(4) DFR < 10

(5) DSA < 10

(6) DSU < 10

Six evening news spots available:

(7) EFR < 6

(8) ESA < 6

(9) ESU < 6

At least 5 ads per day:

(10) DFR + EFR > 5

(11) DSA + ESA > 5

(12) DSU + ESU + GSU > 5

Only two Sunday game-time ad spots available:

Marketing Application-Media Selection

(13) GSU < 2

Spend no more than $50,000 on Friday:

(14) 5000DFR + 7000EFR < 50000

Spend no more than $75,000 on Saturday:

(15) 5000DSA + 7000ESA < 75000

Spend no more than $282,000 in total:

(16) 5000DFR + 5000DSA + 5000DSU + 7000EFR + 7000ESA + 7000ESU + 100000GSU7 < 282000

Non-negativity:

DFR, DSA, DSU, EFR, ESA, ESU, GSU > 0