Question: Harold Grey owns a small farm in the Salinas Valley that grows apricots. The apricots are 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 will be as follows:

                        Forecasted Demand

Year                   (thousand of packages)

1                                300

2                                120

3                                200

4                                110

5                                135

Assume that each worker stays on the job for at least one year, and that Grey currently 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 to 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.

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 part (a).

c. Formulate this as a linear program.

d. Solve the problem and round-off the solution and determine the cost of the resulting plan.