There is only one copying machine in the student lounge of the business school. Students arrive at the rate of $\lambda=$ 40 per hour (according to a Poisson distribution). Copying takes an average of 40 seconds, or $\mu=90$ per hour (according to a negative exponential distribution). Compute the following:

The percentage of time that the machine is used.

Calls arrive at Lynn Ann Fish's hotel switchboard at a rate of 2 per minute. The average time to handle each is 20 seconds. There is only one switchboard operator at the current time. The Poisson and negative exponential distributions appear to be relevant in this situation.

What is the probability that the operator is busy?

There is only one copying machine in the student lounge of the business school. Students arrive at the rate of $\lambda=$ 40 per hour (according to a Poisson distribution). Copying takes an average of 40 seconds, or $\mu=90$ per hour (according to a negative exponential distribution). Compute the following:

The average time spent waiting in the queue.

The pharmacist at Arnold Palmer Hospital, Wende Huehn-Brown, receives 12 requests for prescriptions each hour, Poisson distributed. It takes her a mean time of 4 minutes to fill each, following a negative exponential distribution. Use the waitingline table, Table D.5, and $W_q=L_q / \lambda$, to answer these questions.

How long will the average prescription spend in the queue?

Automobiles arrive at the drive-through window at the downtown Baton Rouge, Louisiana, post office at the rate of 4 every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are negative exponentially distributed.

What is the average time a car is in the queue?

Calls arrive at Lynn Ann Fish's hotel switchboard at a rate of 2 per minute. The average time to handle each is 20 seconds. There is only one switchboard operator at the current time. The Poisson and negative exponential distributions appear to be relevant in this situation.

What is the average number of calls waiting to be answered?

Customers arrive at Rich Dunn's Styling Shop at a rate of 3 per hour, distributed in a Poisson fashion. Rich's service times follow a negative exponential distribution, and Rich can complete an average of 5 haircuts per hour.

Find the percentage of time that Rich is busy.

A company produces two very similar products that go through a three-step sequence of fabrication, assembly, and packaging. Each step requires one day for a lot to be completely processed and moved to the next department. Processing requirements for the departments (hours per unit) are

Department capacities are all 700 hours of labor and 500 hours of machine time, except Friday, when capacities are 200 hours for both labor and machine time. The following production schedule is for next week:

a. Determine the labor and machine capacity requirements for each product and the total load for each department for each day. Ignore changeover time. b. Evaluate the projected loading for the first three days of the week. Is the schedule feasible? What do you suggest for balancing the load?

Customers arrive at Rich Dunn's Styling Shop at a rate of 3 per hour, distributed in a Poisson fashion. Rich's service times follow a negative exponential distribution, and Rich can complete an average of 5 haircuts per hour.

Find the average time a customer spends in the shop.

Customers arrive at Rich Dunn's Styling Shop at a rate of 3 per hour, distributed in a Poisson fashion. Rich's service times follow a negative exponential distribution, and Rich can complete an average of 5 haircuts per hour.

Find the average time a customer waits until it is his or her turn.

Customers arrive at Rich Dunn's Styling Shop at a rate of 3 per hour, distributed in a Poisson fashion. Rich's service times follow a negative exponential distribution, and Rich can complete an average of 5 haircuts per hour.

Find the average number of customers in the shop.

Customers arrive at Rich Dunn's Styling Shop at a rate of 3 per hour, distributed in a Poisson fashion. Rich's service times follow a negative exponential distribution, and Rich can complete an average of 5 haircuts per hour.

Find the average number of customers waiting for haircuts.

Janson’s Department Store in Stark, Ohio, maintains a successful catalog sales department in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the catalog department are answered automatically by a recording machine and asked to wait. As soon as the clerk is free, the party who has waited the longest is transferred and serviced first. Calls come in at a rate of about 12 per hour. The clerk can take an order in an average of 4 minutes. Calls tend to follow a Poisson distribution, and service times tend to be negative exponential.

The cost of the clerk is $\$ 10$ per hour, but because of lost goodwill and sales, Janson's loses about $\$ 25$ per hour of customer time spent waiting for the clerk to take an order.

Pamela Janson is considering adding a second clerk to take calls. The store's cost would be the same $\$10$ per hour. Should she hire another clerk? Explain your decision.

The following table details the tasks required for Indiana-based Frank Pianki Industries to manufacture a fully portable industrial vacuum cleaner. The times in the table are in minutes. Demand forecasts indicate a need to operate with a cycle time of 10 minutes.

Draw the appropriate precedence diagram for this production line.