LP29. Suppose five daily newspapers are published in a certain country, each paper covering some of the twelve regions of the country as shown in the following table: Newspaper | Regions covered | Cost of advertisment | Expected benefit $3000 1,2, 4, 9 2,3, 6, 10, 12 4, 5, 7, 10 1 $15000 $7000 $4000 $5000 $16000 $10000 $19000 2 3 2, 3, 7, 10, 11 4, 5, 6, 8, 9, 11, 12 4 5 $8000 $20000 The marketing manager wants to find a minimum total cost of advertisment such that (a) The advertisment covers the whole country. (b) The sum of expected benefits from advertisment will be at least the triple of the cost of advertisment. Formulate the manager's problem as an integer linear program and solve it.

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LP29. Suppose five daily newspapers are published in a certain country, each paper covering some of the twelve
regions of the country as shown in the following table:
Newspaper | Regions covered | Cost of advertisment | Expected benefit
$3000
1,2, 4, 9
2,3, 6, 10, 12
4, 5, 7, 10
2,3, 7, 10, 11
1
$15000
$7000
$4000
$5000
$16000
$10000
$19000
2
3
4
4, 5, 6, 8, 9, 11, 12
$8000
$20000
The marketing manager wants to find a minimum total cost of advertisment such that
(a) The advertisment covers the whole country.
(b) The sum of expected benefits from advertisment will be at least the triple of the cost of advertisment.
Formulate the manager's problem as an integer linear program and solve it.
Transcribed Image Text:LP29. Suppose five daily newspapers are published in a certain country, each paper covering some of the twelve regions of the country as shown in the following table: Newspaper | Regions covered | Cost of advertisment | Expected benefit $3000 1,2, 4, 9 2,3, 6, 10, 12 4, 5, 7, 10 2,3, 7, 10, 11 1 $15000 $7000 $4000 $5000 $16000 $10000 $19000 2 3 4 4, 5, 6, 8, 9, 11, 12 $8000 $20000 The marketing manager wants to find a minimum total cost of advertisment such that (a) The advertisment covers the whole country. (b) The sum of expected benefits from advertisment will be at least the triple of the cost of advertisment. Formulate the manager's problem as an integer linear program and solve it.
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