Question

The Ponchatrain Bridge is a​ 16-mile toll bridge that crosses Lake Ponchatrain in New Orleans.​ Currently, there are 7 toll​ booths, each staffed by an employee. Since Hurricane​ Katrina, the Port Authority has been considering replacing the employees with machines. Many factors must be considered because the employees are unionized. ​ However, one of the Port​ Authority's concerns is the effect that replacing the employees with machines will have on the times that drivers spend in the system. Customers arrive to any one toll booth at a rate of 12 per minute. In the exact change lanes with​ employees, the service time is essentially constant at 4 seconds for each driver. With​ machines, the average service time would still be 4 ​seconds, but it would be negative exponential rather than​ constant, because it takes time for the coins to rattle around in the machine.

For the​ "Exact Change​ Lane" with employee

The average time driver spends waiting to pay the toll ​= __ seconds​ (round your response to two decimal​ places).

The average time spent by a driver in the toll system​ (waiting and​ paying) ​= __ seconds​ (round your response to two decimal​ places)

The average number of drivers waiting in the line to pay the toll at a toll

booth​=__ drivers​ (round your response to two decimal​ places).

The average number of drivers at any toll​ booth, namely, in the system ​= __ drivers​ (round your response to two decimal​ places).

For the lane with the proposed machine

The average time driver spends waiting to pay the toll ​= __ seconds​ (round your response to two decimal​ places).

The average time spent by a driver in the toll system​ (waiting and​ paying) ​= __ seconds​ (round your response to two decimal​ places).

The average number of drivers waiting in the line to pay the toll at a toll booth​= __ drivers​ (round your response to two decimal​ places).

The average number of drivers at any toll​ booth, namely, in the system drivers​ __ (round your response to two decimal​ places).

As a result of proposed​ change, the average time spent per driver waiting in the line to pay the toll increases by __ (round your response to the nearest whole​ number).

As a result of proposed​ change, the average time spent per driver in the toll system increases by __ (round your response to the nearest whole​ number).

As a result of proposed​ change, the average number of drivers waiting in the line to pay the toll increases by (round your response to the nearest whole​ number).

As a result of proposed​ change, the average number of drivers at any toll booth increases by​ (round your response to the nearest whole​ number).

Answer 1