Question

A gas station with only one gas pump employs the following policy: If a customer has to wait to buy the gasoline, the price is $3.50 per gallon. If she does not have to wait to buy the gasoline, the price is $4.00 per gallon. Customers arrive according to a Poisson process with a mean rate of 20 per hour. Service times at the pump have an exponential distribution with a mean of 2 minutes. Arriving customers always wait until they can eventually buy gasoline. Determine the expected price (in $) of gasoline per gallon. Group of answer choices

Answer 1

Answer:

Explanation:

The arrival rate (λ) = 20 customers per hour. Since the service times at the pump have an exponential distribution with a mean of 2 minutes, therefore the service rate (μ) = 60 / 2 = 30 customers per hour.

The probability of the no  customers being in the system(P₀) is given as:

$P_0=1-\frac{\lambda}{\mu} =1-\frac{20}{30}=1-0.67=0.33$

If no customer is in the system we can sell gasoline for $4 /gallon to the next customer. The expected price p of gasoline is given by:

$P=P_0*4+(1-P_0)3.5=0.33*4+(1-0.33)3.5=1.32+2.345=3.665$

P = $3.665 per gallon