People arrive at a college admissions office at rate 1 per minute, and the arrival is a Poisson process. When k people have arrive, a tour starts. Student tour guides are paid $20 for each tour they conduct. The college estimates that it loses ten cents in good will for each minute a person waits. What tour group (not counting the guide) minimizes the average cost per person?

Question

Mathematics

Ben Estes

6 July, 08:34

People arrive at a college admissions office at rate 1 per minute, and the arrival is a Poisson process. When k people have arrive, a tour starts. Student tour guides are paid $20 for each tour they conduct. The college estimates that it loses ten cents in good will for each minute a person waits. What tour group (not counting the guide) minimizes the average cost per person?

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Answers (1)

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Mitzi · Answer 1

K=20

Step-by-step explanation:

There seem to be no randomness in the question.

At 1 per minutes the arrival rate is fixed.

Then compute the average cost for each person to give a four, adding the cost of guide and time waiting cost ...

Therefore, K is the number of people hoping will show up.

Number of per minute waiting

= 1/2 (K-1) K.

Tour cost 20+1/20 (K-1).

Cost per guest = 20/k + 1/20 (K-1)

If the derivative is set to Zero

K=20