As part of a campaign to promote its annual clearance sale, the Excelsior Company decided to buy television advertising time on Station KAOS. Excelsior's advertising budget is $106,000. Morning time costs $2800/minute, afternoon time costs $1500/minute, and evening (prime) time costs $12,000/minute. Because of previous commitments, KAOS cannot offer Excelsior more than 6 min of prime time or more than a total of 35 min of advertising time over the 2 weeks in which the commercials are to be run. KAOS estimates that morning commercials are seen by 210,000 people, afternoon commercials are seen by 90,000 people, and evening commercials are seen by 610,000 people. How much morning x, afternoon y, and evening z advertising time (in min) should Excelsior buy to maximize exposure, P, of its commercials?

Question

Moshe Mullins

Business

21 July, 23:14

As part of a campaign to promote its annual clearance sale, the Excelsior Company decided to buy television advertising time on Station KAOS. Excelsior's advertising budget is $106,000. Morning time costs $2800/minute, afternoon time costs $1500/minute, and evening (prime) time costs $12,000/minute. Because of previous commitments, KAOS cannot offer Excelsior more than 6 min of prime time or more than a total of 35 min of advertising time over the 2 weeks in which the commercials are to be run. KAOS estimates that morning commercials are seen by 210,000 people, afternoon commercials are seen by 90,000 people, and evening commercials are seen by 610,000 people. How much morning x, afternoon y, and evening z advertising time (in min) should Excelsior buy to maximize exposure, P, of its commercials?

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Answers (1)

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Caesar · Answer 1

To maximize exposure, P, of its commercials:

morning - 26 minutes

afternoon - 0 minutes

everning - 5 minutes

Explanation:

note the following:

x is the morning time (min)

y is the afternoon time (min)

z is the evening time (min)

let > = be greater or equals to and < = less or equals to

we are supposed to maximize > = 210,000x + 90,000y + 610,000z

subject to x + y + z < = 35

$2800x + $1500y + $12,000z < = $106,000

z < = 6

x > = 0

y > = 0

z > = 0

x = 36, y = 0, z = 5

Therefore, to maximize exposure, P, of its commercials:

morning - 26 minutes

afternoon - 0 minutes

everning - 5 minutes