Final answer:
Economic analysis shows that the saving in customer's time may not cover the cost of the new equipment when valued at $20 per hour. However, the decision might depend on the actual value of reduced waiting time and whether the bank wants to meet a service standard of 8 minutes total time spent by the customer.
Step-by-step explanation:
Economic Justification for Leasing New Equipment
In the scenario presented, the average rate of customer arrivals is 40 per hour, which translates to one customer every 1.5 minutes (60 minutes divided by 40 customers). Currently, each teller completes a transaction in 5 minutes, so with 4 tellers, the bank processes customers at a rate of 48 per hour (4 tellers times 12 customers per teller per hour), which is above the arrival rate of 40 per hour. However, if customer waiting time is monetized at $20 per customer per hour, and the new equipment reduces each transaction time to 4 minutes, the new service rate with the equipment would be 60 customers per hour (4 tellers times 15 customers per teller per hour), which significantly exceeds the arrival rate, potentially reducing waiting time.
The cost of the new equipment is $30 per hour. If we assume that the reduced transaction time saves 1 minute per customer, for the 40 customers arriving per hour, this amounts to a total saving of 40 minutes of customer time. Monetized at $20 per hour, this equates to a saving of approximately $13.33 (40 minutes / 60 minutes x $20). This does not cover the cost of the new equipment. Therefore, on an economic basis, leasing the new equipment to save customer's time alone may not be justified unless the waiting time has a greater value than estimated.
In terms of the service standard of 8 minutes in and out of the drive-in facility, the current average service time is 5 minutes plus the average waiting time (which depends on queue length and service rate). Without the exact queue model and service rate calculation, we can't provide a conclusive answer, but if the current waiting time is significantly above 3 minutes on average, the new equipment might be necessary to meet the 8-minute standard.