Production and Operations Analysis by Steven Nahmias and Tava Lennon Olsen 7th E

Question

Production and Operations Analysis by Steven Nahmias and Tava Lennon Olsen 7th Edition Chapter 3 #25

Harold Grey owns a small farm in the Salinas Valley that grows apricots The apricots ate dried on the premises and sold to a number of large supermarket chains Based on past experience and committed contracts, he estimates that sales over the next five years in thousands of packages "ill be as follows. Assume that each worker slays on the job for at least one year, and that Grey current!) has three workers on the payroll. He estimates that he will have 20,000 packages on hand at the end of the current year. Assume that, on the average, each worker is paid $25,000 per year and is responsible for producing 30.000 packages Inventory costs have been estimated lo be 4 cents per package per year, and shortages are not allowed. Based on the effort of interviewing and training new workers. Farmer Grey estimates that it costs $500 for each worker hired Severance pay amounts to $1, 000 per worker. Assuming that shortages are not allowed, determine the minimum constant workforce that he will need over the next five years Evaluate the cost of the plan found in part (a). Formulaic this as a linear program. Solve the problem and round-off the solution and determine the cost of the resulting plan.

Explanation / Answer

months demand no of workdays monthly production/worker no fo workers needed no hired no fired beg. Inv production end inv. Ci= $0.1 Ch=$ 100 Cf=$ 200 1        8,50,000 26                                  8,007 106               70 0 0    13,65,000 5,15,000      51,500.00 7047.06 0 2      12,60,000 24                                  7,391 170 0 0 5,15,000    10,04,651 2,59,651      25,965.12 0.00 0 3        5,10,000 20                                  6,159 83 0 0 2,59,651       8,37,209 5,86,860      58,686.05 0.00 0 4        9,80,000 16                                  4,928 199 0 0 5,86,860       6,69,767 2,76,628      27,662.79 0.00 0 total      36,00,000 86 1,63,813.95 7047.06 0 120 workers in 46 days produced                         17,00,000 cookies hence, production per worker per day 308 cookies avg monthly demand for next 4 months                      9,00,000.00 avg no of workdays per month                                  21.50 hence avg production needed per day                         41,860.47 hence, avg no of workers needed                                     136 current no of workers 100 a) Minimum constant workforce needed to meet the demand every month = 170 , if 136 is kept minimum constant workforce demand for month 2 will not be met.

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