Problem $2.$ Remember Harold Gray from the last homework? 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:

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

two 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 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$)$ Formulate the problem of determining the optimal hiring policy to minimize total cost

as an integer linear program.

$($b$)$ Solve the linear program using linear programming solver. Round the variables in the

resulting solution and determine the cost of the plan you obtain.