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.

constants mean the stopped points or the points on a graph that nothing is changing, hope this

step-by-step explanation:

(2,20) means that the 2 is 2 hours and 20 is 20$. so there both 20$ for 2 hours only the same price. like it says. so, the dunk tank and the bounce house are the same price (20$) for the same amount of time (2 hours).

hope i