Question

In the production shop of a company, the breakdown of the machines is found to be

Poisson distributed with an average rate of 3 machines per hour. Breakdown time at one

machine cost 400 birr per hour to the company. There are two choices before the

company for hiring the repairmen. One of the repairmen is slow but cheap, the other is

fast but expensive. The slow cheap repairman demands 200 birr per hour and will repair

the broken down machines exponentially at the rate of 5 per hour. The fast expensive

man demands 300 birr per hour and will repair machines exponentially at an average rate

of 6 per hour. Which repairman should be hired?

Answer 1

To determine which repairman should be hired, we need to compare the costs of each repairman. The slow cheap repairman has a lower cost per machine, so the company should hire the slow cheap repairman.

Step-by-step explanation:

The repairman that should be hired

To determine which repairman should be hired, we need to compare the costs of each repairman. Let's calculate the total cost for each repairman.

Slow cheap repairman

The slow cheap repairman charges 200 birr per hour and repairs machines at a rate of 5 per hour. The average repair time is 1/5 hours per machine. So, the cost per machine is 200 * 1/5 = 40 birr per machine.

Fast expensive repairman

The fast expensive repairman charges 300 birr per hour and repairs machines at a rate of 6 per hour. The average repair time is 1/6 hours per machine. So, the cost per machine is 300 * 1/6 = 50 birr per machine.

Since the slow cheap repairman has a lower cost per machine, the company should hire the slow cheap repairman.