Warehouse requires different numbers of employee hours on different days of the week. The number of hours required each day is given below. This warehouse can meet its daily labor requirements by using both full-time and part-time employees. During each week a full-time employee works eight hours a day for five consecutive days, and a part-time employee works four hours a day for five consecutive days. A full-time employee costs the post office $17.50 per hour, whereas a part-time employee costs the post office only $12.50 per hour. Labor law requirements limit part-time labor to 30% of weekly labor requirements. Formulate a linear programming model to determine how the South Bay warehouse can meet its daily labor needs at minimal total cost. Assume that fractional numbers of employees can be scheduled.

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Maximum part-time labor 30.00% Full-time hourly rate $17.50 Part-time hourly rate $12.50 Full-time hours per day 8 Part-time hours per day 4 Full-time start Mon Part-time start Mon Full-time start Tues Part-time start Tues Full-time start Wed Part-time start Wed Full-time start Thur Full-time start Fri Full-time start Sat Full-time start Sun Full-time schedule Number of hours full-time Part-time schedule Number of hours part-time Total Hours Worked Hours required Maximum hours worked Total full-time hours worked Total part-time hours worked Maximum part-time allowed Full-time weekly payroll Part-time weekly payroll Total weekly payroll Mon Tues Part-time start Thur Part-time start Fri Part-time start Sat Part-time start Sun Wed Thurs Fri Sat Sun 0 0 0 0 Fri Sat Sun 0 0 0 Mon Tues Wed Thurs >= >= 160 120 = 152 >= 168 >= 104 >= 144 >= 104 Maximum part-time labor 30.00% Full-time hourly rate $17.50 Part-time hourly rate $12.50 Full-time hours per day 8 Part-time hours per day 4 Full-time start Mon Part-time start Mon Full-time start Tues Part-time start Tues Full-time start Wed Part-time start Wed Full-time start Thur Full-time start Fri Full-time start Sat Full-time start Sun Full-time schedule Number of hours full-time Part-time schedule Number of hours part-time Total Hours Worked Hours required Maximum hours worked Total full-time hours worked Total part-time hours worked Maximum part-time allowed Full-time weekly payroll Part-time weekly payroll Total weekly payroll Mon Tues Part-time start Thur Part-time start Fri Part-time start Sat Part-time start Sun Wed Thurs Fri Sat Sun 0 0 0 0 Fri Sat Sun 0 0 0 Mon Tues Wed Thurs >= >= 160 120 = 152 >= 168 >= 104 >= 144 >= 104