Question 1201432: As part of a campaign to promote its annual clearance sale, Excelsior Company decided to buy television advertising time on Station KAOS. Excelsior's television advertising budget is $120,000. Morning time costs $3000/min, afternoon time costs $1000/min, and evening (prime) time costs $12,000/min. Because of previous commitments, KAOS cannot offer Excelsior more than 6 min of prime time or more than a total of 25 min of advertising time over the 2 weeks in which the commercials are to be run. KAOS estimates that morning commercials are seen by 200,000 people, afternoon commercials are seen by 100,000 people, and evening commercials are seen by 600,000 people. How much morning, afternoon, and evening advertising time should Excelsior buy to maximize exposure of its commercials?
morning ? min
afternoon ? min
evening ? min
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i used excel and i used a simplex method solving tool.
both told me that the maximum is 7,000,000 people viewing minutes.
that would be 20 morning commercials with 200,000 people viewing each morning commercial plus 5 evening commercials with 600,000 people viewing each evening commercial.
there were 0 afternoon minutes.
my objective function was 200,000 * the number of morning commercials + 100,000 * the number of afternoon commercials + 600,000 * the number of evening commercials.
this is what i wanted to maximize.
the money results from both tools are in thousands.
7000 is 7000 thousand = 7 million.
120 is 120 thousand.
the excel output is shown below:
the simplex method toool output is shown below:
this could not be solved graphically because it would have required a 3 dimensional graph that, while possible, would have been very difficult to see the results with.
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