Question

A vending machine dispenses hot chocolate or coffee. Service time is 35 seconds per cup and is constant. Customers arrive at a mean rate of 66 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 in minutes

c. Determine the average number of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Average number of customers

Answer 1

Answer:-

Given That:-

A vending machine dispenses hot chocolate or coffee. Service time is 35 seconds per cup and is constant. Customers arrive at a mean rate of 66 per hour, and this rate is Poisson-distributed.

In the question, the below data is provided

= 66 customers/hour

  customers/hour

= 66/102.86

= 0.64

a. Determine the average number of customers waiting in line.

Average number of customers waiting in line  

Putting the vlaue of inthe above equation.

= 0.4096/0.78

li = 0.53 customers

Ti = average number of customers waiting in line/

Ti = 0.53/66

Ti = 0.008 hours

b. Determine the average time customers spend in the system.

The Average time spent in the system

T = 0.008 + 1/102.86

T = 0.018 hours

T = 0.018 * 60 minutes

T = 1.08 munites

c. Determine the average number of customers in the system.

The Average number of cutomers in the system

l = 0.53 + 0.64

l = 1.17 customers

Average number of customers in the system l = 1.17 customers.

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