Nine jobs need to be completed within eight weeks. The number of weeks required to complete each job is given in the file P08_26.xlsx. For example, job 2 requires three weeks. Each job requires 40 hours of labor per week. Each week, 160 hours of regular time labor are available. Up to 40 hours of overtime labor can be purchased each week at a cost of $10 per hour. Additional overtime hours cost $20 per hour.

a. Determine how to minimize the overtime cost incurred in completing the jobs within eight weeks.

b. The same file also lists the due date for each job. For example, job 2 should be completed within six weeks. A penalty of $500 is incurred for each day a job is late. Determine how to minimize the sum of overtime and due date penalties.