Question

I am having trouble finding the correct calculation for the last part of this question:

Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.3 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. Agan's management would like to evaluate two alternatives:

• Use one consultant with an average service time of 8 minutes per customer.
• Expand to two consultants, each of whom has an average service time of 10 minutes per customer.

If the consultants are paid $19 per hour and the customer waiting time is valued at $29 per hour for waiting time prior to service, should Agan expand to the two-consultant system? (NO)

What is the total cost for each scenario? Round your answers to the nearest cent.

The total cost for the first scenario where there is one consultant with an average service time of 8 minutes per customer is $31.83. The total cost for the second scenario where there are two consultants with an average service time of 10 minutes per customer is $ (This is the part I cannot figure out).

Answer 1

There seems to be something wrong with what you have calculated.

First scenario: average service time of 8 minutes per customers.

The arrival rate (lambda) = 2.3 customer per hour

The service rate (mu) = 60/8 = 7.5 customer per hour

Use M/M/1 formulas

Average wait at the queue (Wq) = lambda/(mu*(mu-lambda)) = (2.3)/(7.5*(7.5-2.3)) = 0.058 hours

Now we know that on an average 2.3 customer arriver per hour, they wait 0.058 hour in the queue and the cost of waiting in the queue is $29. This means total waiting cost per hour is 2.3*0.58*29 = 3.86

In addition we need to pay for a single employee $19 per hour.

This means our total cost using a single server system is 3.86+19 = $22.86

Second scenario: average service time of 10 minutes and 2 servers

Arrival rate (lambda) = 2.3

Service rate (mu) = 60/10 = 6

Number of servers (c ) = 2

Now this has a lengthy calculation using the formulas shown below.

Solving that, we will see that

Average wait at the queue (Wq) = 0.006 hours.

Now using the previous logic, the cost of waiting time is 0.006*2.3*29 = 0.40

The wage cost for two employees is 19*2 = 38

This means that the total cost is $38.40