Mega Plantation is a company with about five years of experience in oil palm plantation. The...

 

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Mega Plantation is a company with about five years of experience in oil palm plantation. The company headquarters is in northern Perak. Mega Plantation has an estate which is divided into 7 sectors. Each sector needs a group of workers to carry out oil palm field operations such as harvesting, weeding, applying fertilizer, transporting fresh fruit bunches, etc. The number of workers needed for each sector from Monday to Sunday is shown in the following table. Mon Tue Wed Thu Fri Sat Sun Start on Monday Start on Sector 1 Sector 2 Sector 3 5 6 6 6 3 8 5 Tuesday Start on Wednesday Start on Thursday Start on Friday Start on Saturday Start on Sunday 3 6 2 6 9 Off day Off day 5 6 6 3 Off day Off day 4 9 3 8 6 A worker will need to work for five consecutive days and then rest for two days. If a worker starts. working on Monday, then the worker will work on Monday, Tuesday, Wednesday, Thursday, and Friday. Saturday and Sunday are off days for that worker. The following table shows the working days and off days of workers. Monday Tuesday Wednesday Thursday Friday Sector 4 Sector 5 Sector 6 Sector 7 5 4 Off day Off day 4 8 5 5 7 3 6 7 6 8 7 4 7 5 Off day Off day 7 8 10 5 8 Saturday Sunday Off day off day Off day 9 7 5 6 11 4 8 Off day Off day off day Assuming that you are the estate manager who needs to decide the number of workers for each day in a week. You must make sure that the number of workers is minimum and sufficient to cover the operations in all the 7 sectors. 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. Mega Plantation is a company with about five years of experience in oil palm plantation. The company headquarters is in northern Perak. Mega Plantation has an estate which is divided into 7 sectors. Each sector needs a group of workers to carry out oil palm field operations such as harvesting, weeding, applying fertilizer, transporting fresh fruit bunches, etc. The number of workers needed for each sector from Monday to Sunday is shown in the following table. Mon Tue Wed Thu Fri Sat Sun Start on Monday Start on Sector 1 Sector 2 Sector 3 5 6 6 6 3 8 5 Tuesday Start on Wednesday Start on Thursday Start on Friday Start on Saturday Start on Sunday 3 6 2 6 9 Off day Off day 5 6 6 3 Off day Off day 4 9 3 8 6 A worker will need to work for five consecutive days and then rest for two days. If a worker starts. working on Monday, then the worker will work on Monday, Tuesday, Wednesday, Thursday, and Friday. Saturday and Sunday are off days for that worker. The following table shows the working days and off days of workers. Monday Tuesday Wednesday Thursday Friday Sector 4 Sector 5 Sector 6 Sector 7 5 4 Off day Off day 4 8 5 5 7 3 6 7 6 8 7 4 7 5 Off day Off day 7 8 10 5 8 Saturday Sunday Off day off day Off day 9 7 5 6 11 4 8 Off day Off day off day Assuming that you are the estate manager who needs to decide the number of workers for each day in a week. You must make sure that the number of workers is minimum and sufficient to cover the operations in all the 7 sectors. 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.

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Linear Programming Model for Mega Plantation Worker Scheduling a Formulation Decision Variables Let xij be the number of workers starting on day i and ... View the full answer