Two hot dog vendors at a Georgia Tech football game get a surge of customers arriving as a PPwith rate 10 per minute during halftime. Each vendor takes half a minute on average to serve onecustomer. The waiting line has space for the one or two customers being served plus 15 more towait. If more than 15 are waiting, the line starts to obstruct foot traffic.

• Estimate the number of minutes until foot traffic is obstructed, if the line is empty at the statrt of halftime.

Question

Mathematics

Alexis Guzman

7 September, 04:15

Two hot dog vendors at a Georgia Tech football game get a surge of customers arriving as a PPwith rate 10 per minute during halftime. Each vendor takes half a minute on average to serve onecustomer. The waiting line has space for the one or two customers being served plus 15 more towait. If more than 15 are waiting, the line starts to obstruct foot traffic.

• Estimate the number of minutes until foot traffic is obstructed, if the line is empty at the statrt of halftime.

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Answers (1)

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Colin Hanson · Answer 1

We might expect a foot traffic at the 9 minute mark.

Step-by-step explanation:

We may expect approximately that each new customer arrives at a rate of 60/6 = 10 seconds. The two vendors may serve a total of 4 customers per minute, so we may assume that each minute 2 more customers will be kept waiting. We need more than of 15+2 = 17 customers to be waiting (this includes the 2 ones being served). Thus, we might expect a foot traffic at the 18/2 = 9 minute mark.