ID:201702002
Linear Programing Models: Case Studies
W1-3. The advertising agency promoting the new Bream dishwashing detergent wants to get the
... [Show More] best
exposure possible for the product within the $100,000 advertising budget ceiling placed upon it. To do
so, the agency needs to decide how much of the budget to spend on each of its two most effective
media: (1) television spots during the afternoon hours and (2) large ads in the city's Sunday newspaper.
Each television spot costs $3,000; each Sunday newspaper ad costs $1,250. The expected exposure,
based on industry ratings, is 35,000 viewers for each TV commercial and 20,000 readers for each
newspaper advertisement. The agency director, Mavis Early, knows from experience that it is important
to use both media in order to reach the broadest spectrum of potential Bream customers. She decides
that at least 5 but no more than 25 television spots should be ordered; and that at least 10 newspaper
ads should be contracted. How many times should each of the two media be used to obtain maximum
exposure while staying within the budget? Use linear programming to solve.
TELEVISION SPOTS NEWSPAPER AD
TOTAL BUDGET AVAILABLE $100,000
COST $3,000 $1,250
EXPECTED EXPOSURE 35,000 VIEWERS 20,000 READERS
CONSTRAINTS AT LEAST 5 BUT NO
MORE THAN 25
AT LEAST 10
Objective: obtain maximum exposure while staying within the budget.
Define the decision variables to be:
X1 = Number for TV spots to be ordered.
X2 = Number of newspaper advertisements to be contracted.
Objective function is the total exposure:
Z = 35,000X1 + 20,000X2
Constraints:
1) 3,000 X1 + 1,250 X2 ≤ 100,000 (Total budget available).
2) X1 ≥ 5 (Minimum required TV spots).
3) X2 ≤ 25 (Maximum TV spots allowed).
4) X2 ≥ 10 (Minimum required NP ads).
The LP problem is
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