Problem 7-27 During the campus Spring Fling, the bumper car amusement attraction

Question

Problem 7-27 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 $15 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 40 minutes. Two repairers take 30 minutes, and three take 20 minutes. While these cars are down, lost income is $30 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.) Total cost per hour b. What is the total hourly cost with two repair persons? (Round your intermediate calculations and final answer to 2 decimal places.) Total cost per hour c. What is the total hourly cost with three repair persons? (Round your intermediate calculations and final answer to 2 decimal places.) Total cost per hour

Explanation / Answer

Arrival rate (A) = 1

Service rates are:

S1 for single person = 40 minutes or 1.5 per hour

S2 for two person = 30 minutes or 2 per hour

S3 for three person = 20 minutes or 3 per hour

Average number of customers in system = A/S + A^2/(S*(S-A))

Cost = Cost per hour per person*Number + Average number in system*Lost income per hour

a) Cost with single person = 15*1 + (1/(1.5*(1.5-1)) + 1/1.5)*30 = 75

b) Cost with two person = 15*2 + (1/(2*(2-1)) + 1/2)*30 = 60

c) Cost with three person = 15*3 + (1/(3*(3-1)) + 1/3)*30 = 60

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