Four automobiles have entered Bubba’s Repair Shop for various types of work, ran

Question

Four automobiles have entered Bubba’s Repair Shop for various types of work, ranging from a transmission overhaul to a brake job. The experience level of the mechanics is quite varied, and Bubba would like to minimize the time required to complete all of the jobs. He has estimated the time in minutes for each mechanic to complete each job. Billy can complete job 1 in 400 minutes, job 2 in 90 minutes, job 3 in 60 minutes, and job 4 in 120 minutes. Taylor will finish job 1 in 650 minutes, job 2 in 120 minutes, job 3 in 90 minutes, and job 4 in 140 minutes. Mark will finish job 1 in 480 minutes, job 2 in 120 minutes, job 3 in 80 minutes, and job 4 in 180 minutes. John will complete job 1 in 500 minutes, job 2 in 110 minutes, job 3 in 90 minutes, and job 4 in 150 minutes. Each mechanic should be assigned to just one of these jobs. What is the minimum total time required to finish the four jobs? Who should be assigned to each job?

Show every step and explain why you're doing it

Explanation / Answer

There are a total of 4! combinations in which the 4 jobs can be done.

First job is the most time consuming and should be assigned first

It is assigned to Billy. T = 400

THen fourth job should be assigned and it is assigned to Taylor who does it in 140 minutes.

Between John and Mark.

Job 2 is done by John in 110 minutes and job 3 by Mark in 80 minutes.

Total time = 400+140+110+80 = 730 minutes

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