# Linear Programming Formulation

 Four automobiles have entered Joe’s Repair shop for various types of work, ranging from a transmission overhall to a brake job. The experience level of the mechanics is quite varied and Joe would like to minimize the time required to finish all 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 1 of these jobs. a. Type in the linear programming formulation to this problem. Use the same format style as the formulation in problem 1. b. Who should be assigned to each job? c. What is the minimum total time required to finish the four jobs. d. Billy has requested to be assigned Job 3. Revise the assignments to minimize completion time while fulfilling Billy’s request. What are the assignments and the minimum completion time?