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 $3000/minute, afternoon time costs $1000/minute, and evening (prime) time costs $11,500/minute. Because of previous commitments, KAOS cannot offer Excelsior more than 6 min of prime time or more than a total of 30 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 100,000 people, and evening commercials are seen by 580,000 people. How much morning x, afternoon y, and evening z advertising time (in min) should Excelsior buy to maximize exposure, P, of its commercials?
Formulate but do not solve the following exercise as a linear programming problem.
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 $3000/minute, afternoon time costs $1000/minute, and evening (prime) time costs $11,500/minute. Because of previous commitments, KAOS cannot offer Excelsior more than 6 min of prime time or more than a total of 30 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 100,000 people, and evening commercials are seen by 580,000 people. How much morning x, afternoon y, and evening z advertising time (in min) should Excelsior buy to maximize exposure, P, of its commercials?
| Maximize | P | = |
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subject to the constraints | |
| advertising budget |
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| total time restrictions |
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| evening (prime) time restrictions |
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| x ≥ 0 | |||||
| y ≥ 0 | |||||
| z ≥ 0 |
Given
Budget = $106,000.
Morning time costs $3000/minute,
afternoon time costs $1000/minute,
evening (prime) time costs $11,500/minute
morning commercials are seen by 210,000 people,
afternoon commercials are seen by 100,000 people,
evening commercials are seen by 580,000 people
x is the morning time (min)
y is the afternoon time (min)
z is the evening time (min)
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