Question

During the campus Spring Fling, the bumper car amusement attraction has a problem of cars becoming disabled and in need of repair. Repair personnel can be hired at the rate of $20 per hour, but they only work as one team. Thus, if one person is hired, he or she works alone; two or three people work together on the same repair.

One repairer can fix cars in an average time of 45 minutes. Two repairers take 30 minutes, and three take 20 minutes. While these cars are down, lost income is $40 per hour. Cars tend to break down at the rate of 1.00 per hour.

Management is trying to decide how many repair persons to hire, and has asked you for cost data.

a. What is the total hourly cost with one repair person? (Round your intermediate calculations and final answer to 2 decimal places.)

b. What is the total hourly cost with two repair persons? (Round your intermediate calculations and final answer to 2 decimal places.)

c. What is the total hourly cost with three repair persons? (Round your intermediate calculations and final answer to 2 decimal places.)

d. How many repairers should be hired?

Answer 1

Answer a= When one person is hired

Arrival rate -1 per hour

Repair rate =60/45=1.33 per hour

Avg. no of cars waiting=1/(1.33-1)=3

downtime loss at $40 per hour=40*3=120

cost of repairers=$20

Total cost of hiring one repairer = 120+20=$140

Answer b- When two persons are hired

Arrival rate -1 per hour

Repair rate =60/30=2 per hour

Avg. no of cars waiting=1/(2-1)=1

downtime loss at $40 per hour=40*1=40

cost of repairers=$20*2=40

Total cost of hiring one repairer = 40+40=$80

Answer c- When three persons are hired

Arrival rate -1 per hour

Repair rate =60/20=3 per hour

Avg. no of cars waiting=1/(3-1)=0.5

downtime loss at $40 per hour=40*0.5=20

cost of repairers=$20*3=60

The total cost of hiring one repairer = 60+20=$80

Answer D= as the total cost is least for 2 or 3 repairers so two or three persons can be hired.