The Chamber of Commerce periodically sponsors public service seminars and progra

Question

The Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown: Television Radio Online Constraint Audience per advertisement 100000 16000 35000 Cost per advertisement 1500 $250 $650 Maximum media usage 10 24 14 To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number ofadvertisements authorized. In addition, television should account for at least 10% of the total number of advertiscments authorized. (a) If the promotional budget is limited to $18400, how many commercial messages should berun on each medium to maximize total audience contact? No of commercial Advertisement Alternatives messages Television Radio Online What is the allocation of the budget among the three media? Budget (S) Advertisement Alternatives Television Radio Online What is the total audience reached?

Explanation / Answer

Ans:

The optimal solution value is Z = 1217600
(Television) X1 = 10
(Radio) X2 = 13.6
(online) X3 = 0

Hence,Budget for Television=10*1500=15000

Budget for radio=13.6*250=3400

Total audience reached=10*100000+13.6*16000=1217600

b)

The optimal solution value is Z = 1224000
X1 = 10
X2 = 14
X3 = 0

Audiance contact=10*100000+14*16000=1224000

Increase in audiance=1224000-1217600=6400

MAZIMIZE: 100000 X1 + 16000 X2 + 35000 X3 1500 X1 + 250 X2 + 650 X3 18400
1 X1 + 1 X2 + 1 X3 48
1 X1 + 0 X2 + 0 X3 10
0 X1 + 1 X2 + 0 X3 24
0 X1 + 0 X2 + 1 X3 14
-9 X1 + 1 X2 + 1 X3 0

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