ABS specializes in repair and maintenance of industrial machines.One repair technician has been assigned to five identical grinding machines for repair and maintenance.The machine breaks down after about 20 hours of use,and breakdowns have a Poisson probability distribution.It takes 6 hours to repair a machine,and repair times follow an exponential distribution.Machine downtime costs the company $250 an hour,and the technician is paid $50 an hour.Determine the average cost per hour of downtime if number of technicians is equal to two.
A)$234
B)$432
C)$320
D)$345

Question

Quizplus · Accepted Answer

The average cost per hour of downtime can be calculated as follows:
- Average frequency of breakdowns per grinding machine per hour: λ = 1/20 = 0.05 breakdowns/hour
- Average machine repair time: E(X) = 6 hours
- Average technician cost per hour: Ctechnician = $50/hour
- Average machine downtime cost per hour: Cdown = $250/hour
- Total cost per hour = (number of machines served by one technician x Ctechnician) + (number of breakdowns per hour x E(X) x Cdown)
- With one technician serving five machines, the cost per hour is:
C1 = (5 x $50/hour) + (5 x 0.05 x 6 x $250/hour) = $1,500/hour
- With two technicians serving ten machines, the cost per hour is:
C2 = (2 x 5 x $50/hour) + (10 x 0.05 x 6 x $250/hour) = $1,820/hour
Therefore, the average cost per hour of downtime with two technicians is $320/hour (C2 - C1). The correct answer is C.

ABS Specializes in Repair and Maintenance of Industrial Machines