Question

Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.5 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 $16 per hour and the customer waiting time is valued at $25 per hour for waiting time prior to service, should Agan expand to the two-consultant system?

 

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 $  fill in the blank 2. The total cost for the second scenario where there are two consultants with an average service time of 10 minutes per customer is $  fill in the blank 3.

Note: Use P0 values from Table 11.4 to answer the questions below.

Answer 1

Let's consider the first alternative with one consultant with an average service time of 8 minutes per customer. In other words, the consultant averages 7.5 customers per hour. Remember the arrival rate is 2.5 per hour.

Computation of the average number of customers in the waiting line:

The average number of customers in the waiting line can be computed by using the formula below:

Hence, the average number of customers in the waiting line is 0.1667.

Computation of the average number of customers in the waiting line:

The average number of customers in the waiting line can be computed by using the formula below:

Hence, the average number of customers in the waiting line is 0.50/

Computation of the total cost for the first alternative:

The total cost for the first alternative can be computed as below:

Hence, the total cost for the first alternative is $28.50.

Now consider the second alternative with two consultants, each of whom has an average service time of 10 minutes per customer. In other words, each consultant averages 6 customers per hour.

Computation of the probability that no customers are in the system:

The probability that no customers are in the system can be computed by using the formula below:

Hence, the probability that no customers are in the system is 0.6552.

Computation of the average number of customers in the waiting line:

The average number of customers in the waiting line can be computed by using the formula below:

Hence, the average number of customers in the waiting line is 0.0189.

Computation of the average number of customers in the system:

The average number of customers in the system can be computed by using the formula below:

Hence, the average number of customers in the system is 0.4356.

Computation of the total cost for the second alternative:

The total cost for the second alternative can be computed by using the formula below:

Therefore, the more cost effective alternative is the first one where management uses one consultant with an average service time of 8 minutes per customer.