A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds
ID: 402341 • Letter: A
Question
A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 78 per hour, and this rate is Poisson-distributed.
Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.)
Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Determine the average number in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 78 per hour, and this rate is Poisson-distributed.
a.
Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.)
Average number of customer
b.
Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Average time minutes
c.
Determine the average number in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Average number customers
Explanation / Answer
R= 78
U = 120
a. I = R^2/ 2 U ( U -R ) = 78^2/ 2(120)(120-78) = 0.6035
b. T = I /R+1/U = 0.6035/78 + 1/120 = 0.0160 hrs
c. I = 0.6035 + 78/120 = 1.2535