A vending machine dispenses hot chocolate or coffee. Service time is 20 seconds per cup and is constant. Customers arrive at a mean rate of 64 per hour, and this rate is Poisson-distributed.

A vending machine dispenses hot chocolate or coffee. Service time is 20 seconds per cup and is constant. Customers arrive at a mean rate of 64 per hour, and this rate is Poisson-distributed. Determine:

a.Average number of customers waiting in line.

b.Average time customers spend  in the system.

The average number of customers waiting is 0.196 and average time spend is 0.00862 hr.

Step-by-step explanation:

Given:

Arrival rate, = 64/hr

Service time = 20 sec/cup

Service rate = = per/min = = per/hr

According to the question:

Its a Poisson's distribution of (M/M/1) model.

Formula to be used:

a.Average number of customers waiting in line.

 ⇒  

b.Average time customers spend  in the system.

 ⇒

Solving step-wise:

a.Average no. of customer waiting.

 ⇒  

 ⇒

 ⇒

b.Average time spend.

 ⇒

 ⇒

 ⇒   hr

So the average number of customers waiting is 0.196 and average time spend is 0.00862 hr.

a. the are of the rectangle is 18.25

b. 18.25 times two is 36.50

rae me : d

77

step-by-step explanation: