using the Johnson's rule, determine the optimal sequencing for the following jobs based on their processing times on two machines:

Job a: machine A takes $3$ hours; machine B take $5$ hours

Job b: machine a taken $4$ hours; machine b takes $7$ hours

job c: machines a takes $2$ hours; machines b takes $6$ hours

job d: machine a takes $6$ hours; machine b takes $3$ hours

job e: machine a takes $5$ hours; machine b take $4$ hours

job f: machone a takes $3$ hours; machone b takes $2$ hours

determine a sequence that will minimize the total completion time for these jobs. evaluate and explain the steps in getting the solution.