Four automobiles have entered Bubba's Repair Shop for various types of work, ranging from a transmis$-$ sion 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 $180$ 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?