Question: Harold Grey owns a small farm that grows apricots in the Salinas Valley. The apricots are dried on the premises and then sold to a number of large supermarket chains. Based on past experience and committed contracts, he estimates that the sales over the next five years in thousands of packages will be as follows:
Grey currently has three workers on the payroll. Assume that each worker stays on the job for at least one year. He estimates that he will have 20,000 packages on hand at the end of 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 to be 4 cents per package per year, and shortages are not allowed.
Based on the effort of interviewing and training new workers, Grey estimates that it costs
$500 for each worker hired. Severance pay amounts to $1,000 per worker.
(a) Assuming that shortages are not allowed, determine the minimum constant workforce that he will need over the next five years.
(b) Evaluate the cost of the plan found in (a).
(c) Develop a linear-programming model for the least-cost production plan.