Problem 6 (LP-Employee Scheduling): SET UP ONLY (You must use the ATTACHED Excel Grid) Manfred Leaks manages a large discount store. His biggest problem has been scheduling cashiers so that he hasan adequate number without having too many. The store is open from 9 a.m. 109 p.m. each day of the week. Based on historical data, he found that the customer patterns for Monday to Thursday are essentially the same, but those for Friday, Saturday, and Sunday are all different. He divided the day into three four-hour segments and estimated at Jeast how many cashiers were needed for each time period for each day of the week. These are given in the following table. Day of Weck 9 am to 1 pm I pm to 5 pm 5pm to 9pm Mon-Thur 6 5 8 3 8 Sat 10 14 7 Sun 4 12 6 Employees must work continuous eight-hour shifts beginning at 9 a.m. or I p., and their weekly schedules must be made up of five consecutive days of work with two consecutive days off and they work the same houn each workday). Manfred would like to devise weekly schedules that will minimire the total number of cashiers needed. but the schedules must be such that the minimum cashier requirements in the table are satisfied Set up Manfred's problem as an LP model with an objective function, the Saturday and Sunday.comstraints. and the non-negativity constraints. HINTS: 1. There are 14 possible schedules. There is one variable corresponding to each schedule. 2. Use the following notation forthis problem: Let Xij - # of cashiers who work shin i on weekly schedule j, where i - I means 9a.m. - 5p.m.and i 2 means 1 p.m.-9p.m. j - I means the cashier works Mon-Fri: j - 2 means the cashier works Tue-Sat: j - 3 means the cashier works Wed-Sun: j - 4 means the cashier works Thur-Mon: j - 5 means the cashier works Fri-Tue: j - 6 means the cashier works Sat-Wed: and j-7 means the cashier works Sun-Thur. Thus, X. - # of cashiers who work Monday - Friday from 9am-5pm X12= # of cashiers who work Tuesday - Saturday from 9am - 5p.m; and so on, Xo1 # of cashiers who work Monday - Friday from 1p.m. - 9pm. X22 - # of cashiers who work Tuesday - Saturday from 1 p.m.- 9p.m., and so on, 3. There are a total of consta in sanan fimm the non-negativity constraints. There are three constraints each for rint for PROBLEM 6 (EMPLOYEE SCHEDULING PROBLEM) MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY 9-5 pm 1pm-9pm 9am-5pm 1pm-9pm 9 am - 5pm 1pm pm 9 am - 5pm 1pm-9pm 9am-5pm 1pm-9pmam - 5 pm 1pm-9pm 9am-5pm tom. 9 pm Problem 6 (LP-Employee Scheduling): SET UP ONLY (You must use the ATTACHED Excel Grid) Manfred Leaks manages a large discount store. His biggest problem has been scheduling cashiers so that he hasan adequate number without having too many. The store is open from 9 a.m. 109 p.m. each day of the week. Based on historical data, he found that the customer patterns for Monday to Thursday are essentially the same, but those for Friday, Saturday, and Sunday are all different. He divided the day into three four-hour segments and estimated at Jeast how many cashiers were needed for each time period for each day of the week. These are given in the following table. Day of Weck 9 am to 1 pm I pm to 5 pm 5pm to 9pm Mon-Thur 6 5 8 3 8 Sat 10 14 7 Sun 4 12 6 Employees must work continuous eight-hour shifts beginning at 9 a.m. or I p., and their weekly schedules must be made up of five consecutive days of work with two consecutive days off and they work the same houn each workday). Manfred would like to devise weekly schedules that will minimire the total number of cashiers needed. but the schedules must be such that the minimum cashier requirements in the table are satisfied Set up Manfred's problem as an LP model with an objective function, the Saturday and Sunday.comstraints. and the non-negativity constraints. HINTS: 1. There are 14 possible schedules. There is one variable corresponding to each schedule. 2. Use the following notation forthis problem: Let Xij - # of cashiers who work shin i on weekly schedule j, where i - I means 9a.m. - 5p.m.and i 2 means 1 p.m.-9p.m. j - I means the cashier works Mon-Fri: j - 2 means the cashier works Tue-Sat: j - 3 means the cashier works Wed-Sun: j - 4 means the cashier works Thur-Mon: j - 5 means the cashier works Fri-Tue: j - 6 means the cashier works Sat-Wed: and j-7 means the cashier works Sun-Thur. Thus, X. - # of cashiers who work Monday - Friday from 9am-5pm X12= # of cashiers who work Tuesday - Saturday from 9am - 5p.m; and so on, Xo1 # of cashiers who work Monday - Friday from 1p.m. - 9pm. X22 - # of cashiers who work Tuesday - Saturday from 1 p.m.- 9p.m., and so on, 3. There are a total of consta in sanan fimm the non-negativity constraints. There are three constraints each for rint for PROBLEM 6 (EMPLOYEE SCHEDULING PROBLEM) MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY 9-5 pm 1pm-9pm 9am-5pm 1pm-9pm 9 am - 5pm 1pm pm 9 am - 5pm 1pm-9pm 9am-5pm 1pm-9pmam - 5 pm 1pm-9pm 9am-5pm tom. 9 pm