Altug's Coffee Shop decides to install an automatic coffee vending machine outside one of its stores to reduce the number of people standing in line inside. Mehmet Altug charges $3.50 per cup. However, it takes too long for people to make change. The service time is a constant 4.00 minutes, and the arrival rate is 12 per hour (Poisson distributed).
a. The average wait time in the line
b. Mehmet raises the price to $5 per cup and takes 60 seconds off the service time. However, because the coffee is now so expensive, the arrival rate drops to 10 per hour.
c. What is theaverage number of customers waiting in the line.

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cancinodavidq cancinodavidq · Answer 1 · 2019-11-10T20:50:50+01:00

Answer:

a. Wₙ = 0.1333 hours or 8 minutes

b. The average number of people in line is 1,6

c. average wait time is 0.0083 hours or 0.5 minutes

Explanation:

The arival rate is λ and μ service rate.

μ= 60/4 = 15 cars/hour

Arrival rate is 12 per hour

a. Using the given formula Wₙ =λ / 2μ(μ-λ)

Wₙ =12 / 2*15*(15-12) = 12/90 = 0.1333 hours or 8 minutes

b. Determine Lₙ = Wₙ =λ[tex]λ^{2}[/tex] / 2μ(μ-λ)

Lₙ=12^2/2*15*(15-12) = 1,6

The average number of people in line is 1,6

c. μ= 60/2 = 30 cars/hour

Wₙ =10 / 2*30*(30-10) = 10/(60*20) = 0.0083 hours or 0.5 minutes

Hence average wait time is 0.0083 hours or 0.5 minutes