Please solve it as a Linear Programming Model with Detailed steps

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MSCI 2150 MONTH XX, 20XX Page 2 of 13 (1.) Travis, Johnson, the new president of Johnson Groceries, who recently completed an MBA at the University of Manitoba, has decided to keep his store open 24 hours a day. Travis has been able to make the necessary arrangements with vendors, trucking compa- nies, and local banks for the expanded store operating hours. One of Johnson Groceries most nagging problems has been scheduling of workers. The most critical problem fac- ing Travis is determining the daily schedule for cashiers and baggers. Based on Johnson Groceries and other 24-hour stores experiences, Travis has determined the minimum necessary labor for each 4-hour period of the day: Time Period Cashiers Baggers 8 a.m-Noon 3 5 Noon-4p.m 4 4 4 p.m-8 p.m 6 6 8 p.m-Midnight 3 3 Midnight-4 a.m 1 2 4 a.m-8 a.m 2 7 One of the factors complicating the problem is that cashiers and baggers are not inter- changeable. Cashiers need special training for dealing with money and operating the cash register, while baggers need physical strength to handle stocking carts and heavy goods. Johnson Groceries only employs fulltime staff, who work continuous 8-hour shifts. Employees usually report for work at 8 a.m., noon, 4 p.m., 8 p.m., midnight, and 4 a.m. to begin their 8- hour shifts. Wages vary by time frame: Time Period Cashiers Baggers $12.00 $10.80 8 a.m-Noon Noon-4p.m 4 p.m-8 p.m 12.00 10.80 12.60 12.00 8 p.m-Midnight 13.80 13.20 Midnight-4 a.m 15.00 14.40 4 a.m-8 a.m 14.40 13.80 Travis believes that the total number of cashiers and baggers should not be more than 60. He, also believes that there should be more baggers than cashiers. The decision problem is to determine how many cashiers and baggers to schedule for work in order to meet minimum manpower requirements of the store and also minimize total daily wages. Decision Variables: Travis attempts to determine the number of cashiers and bag- gers who will report at the beginning of each 4-hour segment during the 24-hour period. The variables can be defined as follows. I number of cashiers reporting to work during the day at the ith 4-hour intervals starting at 8 a.m. (i=1,2,...,6) Vi = number of baggers reporting to work during the day at the ith 4-hour intervals starting at 8 a.m. (i=1,2,...,6) 15 Points Formulate as a linear programming model