4.) A job shop needs to assign 5 jobs to 5 workers. The time (in minutes) of performing a job is a function of the skills of the workers; these expected completion times are shown in the table at the right. a. Using the Hungarian Method discussed in class, determine the assignment that minimizes the total time necessary to complete all jobs. b. Assuming that jobs are going to be started at the same time and performed simultaneously, a more sensible objective function is to minimize the time at which all jobs are completed. For example, if one decides to assign Job 1 to Worker 1, Job 2 to Worker 2, Job 3 to Worker 3, Job 4 to Worker 4, and Job 5 to Worker 5, all jobs are completed at time CT = Max{37, 61, 75, 27, 77} = 77 min. Determine the assignment that minimizes the time at which all jobs are completed. This problem has a different objective function than the problem in (a) consequently it cannot be solved by the Hungarian Method, but it can be solved by linear programming. Formulate a linear programming model to solve this problem (define the decision variables, objective function, and constraints) C. Solve the LP model in (b) using Excel.

Fig: 1