A national sales company is planning to conduct a weeklong sales meeting in San
ID: 3101950 • Letter: A
Question
A national sales company is planning to conduct a weeklong sales meeting in San Francisco on August 14. On July 14, for a weeklong trip one month from that date, the lowest round trip airfare from New York City (NYC) to San Francisco is $347 and the lowest round-trip airfare from Chicago to San Francisco is $331. There are 28 sales representatives based in NYC and 22 sales representatives based in Chicago who could travel to San Francisco for this meeting, a total of at least 40 sales representatives from Chicago and NYC must attend this meeting with at least 12 from Chicago and at least 16 from NYC. How many sales representatives based in NYC and how many sales representatives based in Chicago should be sent to the San Francisco sales meeting, so as to minimize the total airfare? What is the minimum total airfare?The number of sales representatives from NYC =
The number of sales representatives from Chicago =
The minimum airfare = $
Give the last answer without commas.
Explanation / Answer
OK, so it costs $347 to go from NYC to California and $331 to go from Chicago. Since it's cheaper to fly out from Chicago, we want the most sales reps to come from Chicago, since it's cheaper. However, there are only 22 sales reps from Chicago, so that's the maximum number we can bring. Thus, the number we have to bring from NYC is 40 (the number of reps necessary) - 22, or 18. They'd pay the more expensive NYC fare of $347. Our total cost would be (Chicago people * 331) + (NYC people * 347) = (22*331)+(18*347) = 13528 dollars I really hope this helped! The other restrictions (at least 12 from Chicago and 16 from NYC) end up being irrelevant. The main point of the problem was just to realize that you need to maximize the number of people coming from Chicago, and then solving the problem from there.
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