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need help with details
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answerhappygod
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need help with details
need help with details
ABC Supermarket is a busy grocery store that has requirements for between 10 to 18 cashiers depending on the time of day. Lunchtime, from noon to 2 p.m., and evening, from 5 p.m. to 6 p.m. are usually busiest. The table below indicates the cashiers needed at various hours that the store is open: Time Period 9 a.m. 10 a.m. 10 a.m. 11 a.m. 11 a.m. 12 noon 12 noon - 1 p.m. 1 p.m. - 2 p.m. 2 p.m. -3 p.m. 3 p.m. 4 p.m. Number of Cashiers Required 15 10 12 18 18 16 12 Time Period 4 p.m. - 5 p.m. 5 p.m. - 6 p.m. 6 p.m. -7 p.m. 7 p.m. -8 p.m. 8 p.m. - 9 p.m. 9 p.m. 10 p.m. Number of Cashiers Required 15 18 16 10 12 12 The store now employs 27 full-time cashiers, but many people are on its roster of available part-time employees. A part-time employee must put in exactly 4 hours per day but can start anytime between 9 a.m. and 6 p.m. Part-timers are a fairly inexpensive labour pool because no retirement or lunch/dinner benefits are provided to them. Full-timers, on the other hand, are divided into two groups, one group (i.e. 15 full-timers) works from 9 a.m. to 4 p.m., and the other group (i.e. 12 full-timers) works from 4 p.m. to 10 p.m. Both group of full-timers are allowed 1 hour for lunch/dinner. For the group of full- timers who work from 9 a.m. to 4 p.m., half of the full-timers eat at 11 a.m., and the other half eat at 12 noon). For the group of full-timers who work from 4 p.m. to 10 p.m., half of the full-timers eat at 6 p.m., and the other half eat at 7 p.m.). By the corporate policy, the store limits part-time hours to a maximum of 50% of the day's total requirement. Part-timers earn RM 7.50 per hour, whereas full-timers earn RM 75 per day. The management would like to set a schedule, using Linear Programming, that would minimize its total man-power costs. One or more full-timers will be trained to perform other job/task within the store if it is profitable to do so. a. Formulate a linear programming model for this problem. b. Use a software package based on the simplex method (e.g. Excel Solver) to solve the problem.
ABC Supermarket is a busy grocery store that has requirements for between 10 to 18 cashiers depending on the time of day. Lunchtime, from noon to 2 p.m., and evening, from 5 p.m. to 6 p.m. are usually busiest. The table below indicates the cashiers needed at various hours that the store is open: Time Period 9 a.m. 10 a.m. 10 a.m. 11 a.m. 11 a.m. 12 noon 12 noon - 1 p.m. 1 p.m. - 2 p.m. 2 p.m. -3 p.m. 3 p.m. 4 p.m. Number of Cashiers Required 15 10 12 18 18 16 12 Time Period 4 p.m. - 5 p.m. 5 p.m. - 6 p.m. 6 p.m. -7 p.m. 7 p.m. -8 p.m. 8 p.m. - 9 p.m. 9 p.m. 10 p.m. Number of Cashiers Required 15 18 16 10 12 12 The store now employs 27 full-time cashiers, but many people are on its roster of available part-time employees. A part-time employee must put in exactly 4 hours per day but can start anytime between 9 a.m. and 6 p.m. Part-timers are a fairly inexpensive labour pool because no retirement or lunch/dinner benefits are provided to them. Full-timers, on the other hand, are divided into two groups, one group (i.e. 15 full-timers) works from 9 a.m. to 4 p.m., and the other group (i.e. 12 full-timers) works from 4 p.m. to 10 p.m. Both group of full-timers are allowed 1 hour for lunch/dinner. For the group of full- timers who work from 9 a.m. to 4 p.m., half of the full-timers eat at 11 a.m., and the other half eat at 12 noon). For the group of full-timers who work from 4 p.m. to 10 p.m., half of the full-timers eat at 6 p.m., and the other half eat at 7 p.m.). By the corporate policy, the store limits part-time hours to a maximum of 50% of the day's total requirement. Part-timers earn RM 7.50 per hour, whereas full-timers earn RM 75 per day. The management would like to set a schedule, using Linear Programming, that would minimize its total man-power costs. One or more full-timers will be trained to perform other job/task within the store if it is profitable to do so. a. Formulate a linear programming model for this problem. b. Use a software package based on the simplex method (e.g. Excel Solver) to solve the problem.